In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we...In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we classify these hypersurfaces as not being of a flat affine metric.In particular,2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.展开更多
In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If the...In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1).展开更多
In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvatu...In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvature 1. At the same time, the results on Sasaki manifolds which are given by Miyazaawa and Yamagushi are generalized to K-contact manifolds.展开更多
The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li[2]is generallied,but the method...The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li[2]is generallied,but the method is completely different. Meanwhile,we get better conclusion than that of [3].We also research the Pinching problem for sectional curvature on compact minimal submanifolds in a unit sphere, partially improving the results of S.T.Yan[4].展开更多
In a Robertson-Walker geometry conformally coupled to a scalar field with inflation potential V(φ)=M^(4)-(1/4)λ φ^(4),we investigate the classical evolution of a universe.The exact solutions in the model have been ...In a Robertson-Walker geometry conformally coupled to a scalar field with inflation potential V(φ)=M^(4)-(1/4)λ φ^(4),we investigate the classical evolution of a universe.The exact solutions in the model have been found.It is shown that in the region where the value of the φ field is 0<φ<φ_(max),(φ_(max) is the solution of V(φ)=0),there is inflation.This model can lead to successful inflation with λ~10^(-9),rather than 10^(-13) as previously reported.展开更多
Let N n+p be an (n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p . Instead of (n+p)-dimensional unit sphere, we ge...Let N n+p be an (n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p . Instead of (n+p)-dimensional unit sphere, we generalize Pinching Theorems about submanifolds in unit sphere and get theorems about submanifolds in locally symmetric and conformally flat Riemannian manifold.展开更多
In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in a Locally symmetric and conformally flat Riemannian mainfold N^(+p).When N^(+p)is a space S_(1)^(+p) of constant curvature,our theo...In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in a Locally symmetric and conformally flat Riemannian mainfold N^(+p).When N^(+p)is a space S_(1)^(+p) of constant curvature,our theorems reduce to the theorems of[1],[2].展开更多
We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-e...We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-eigenvalues of conformal flat Einstein manifold have also been discussed,and the conformal the invariance of M-eigentriple has been found.We also reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold.We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely.We also give an example to compute the Meigentriple of de Sitter spacetime which is well-known in general relativity.展开更多
We review the (2 + 1)-dimensional Baňados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3 + 1)-dimensional spacetime. For the matter content we use a scalar-gauge field. The me...We review the (2 + 1)-dimensional Baňados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3 + 1)-dimensional spacetime. For the matter content we use a scalar-gauge field. The metric is written as <img src="Edit_be2cdfd9-fda6-4846-b64d-4d1062f9964e.bmp" alt="" /> where the <em>dilaton</em> field <span style="white-space:nowrap;"><span style="white-space:nowrap;">ω</span></span> contains all the scale dependencies and where <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" /> represents the “un-physical” spacetime. A numerical solution is presented and shows how the dilaton can be treated on equal footing with the scalar field. The location of the apparent horizon and ergo-surface depends critically on the parameters and initial values of the model. It is not a hard task to find suitable initial parameters in order to obtain a regular and singular free <img src="Edit_5d830100-019b-4a6a-82e7-deefdf327ecc.bmp" alt="" /> out of a BTZ-type solution for <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" style="white-space:normal;" />. In the vacuum situation, an exact time-dependent solution in the Eddington-Finkelstein coordinates is found, which is valid for the (2 + 1)-dimensional BTZ spacetime as well as for the uplifted (3 + 1)-dimensional BTZ spacetime. While <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" style="white-space:normal;" /> resembles the standard BTZ solution with its horizons, <img src="Edit_5d830100-019b-4a6a-82e7-deefdf327ecc.bmp" alt="" style="white-space:normal;" /> is flat. The dilaton field becomes an infinitesimal renormalizable quantum field, which switches on and off Hawking radiation. This solution can be used to investigate the small distance scale of the model and the black hole complementarity issues. It can also be used to describe the problem of how to map the quantum states of the outgoing radiation as seen by a distant observer and the ingoing by a local observer in a one-to-one way. The two observers will use a different conformal gauge. A possible connection is made with the antipodal identification and unitarity issues. This research shows the power of conformally invariant gravity and can be applied to bridge the gap between general relativity and quantum field theory in the vicinity of the horizons of black holes.展开更多
This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole...This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole model with anisotropic fluid under Gaussian and Lorentzian distributions.The primary objective is to derive wormhole solutions while considering the influence of the shape function on model parameters under Gaussian and Lorentzian distributions.The resulting shape function satisfies all the necessary conditions for a traversable wormhole.Furthermore,we analyze the characteristics of the energy conditions and provide a detailed graphical discussion of the matter contents via energy conditions.Additionally,we explore the effect of anisotropy under Gaussian and Lorentzian distributions.Finally,we present our conclusions based on the obtained results.展开更多
Electromagnetic interference shielding(EMI SE)modules are the core com-ponent of modern electronics.However,the tra-ditional metal-based SE modules always take up indispensable three-dimensional space inside electroni...Electromagnetic interference shielding(EMI SE)modules are the core com-ponent of modern electronics.However,the tra-ditional metal-based SE modules always take up indispensable three-dimensional space inside electronics,posing a major obstacle to the integra-tion of electronics.The innovation of integrating 3D-printed conformal shielding(c-SE)modules with packaging materials onto core electronics offers infinite possibilities to satisfy ideal SE func-tion without occupying additional space.Herein,the 3D printable carbon-based inks with various proportions of graphene and carbon nanotube nanoparticles are well-formulated by manipulating their rheological peculiarity.Accordingly,the free-constructed architectures with arbitrarily-customized structure and multifunctionality are created via 3D printing.In particular,the SE performance of 3D-printed frame is up to 61.4 dB,simultaneously accompanied with an ultralight architecture of 0.076 g cm^(-3) and a superhigh specific shielding of 802.4 dB cm3 g^(-1).Moreover,as a proof-of-concept,the 3D-printed c-SE module is in situ integrated into core electronics,successfully replacing the traditional metal-based module to afford multiple functions for electromagnetic compatibility and thermal dissipa-tion.Thus,this scientific innovation completely makes up the blank for assembling carbon-based c-SE modules and sheds a brilliant light on developing the next generation of high-performance shielding materials with arbitrarily-customized structure for integrated electronics.展开更多
The application of thermoelectric devices(TEDs)for personalized thermoregulation is attractive for saving energy while balancing the quality of life.TEDs that directly attach to human skin remarkably minimized the ene...The application of thermoelectric devices(TEDs)for personalized thermoregulation is attractive for saving energy while balancing the quality of life.TEDs that directly attach to human skin remarkably minimized the energy wasted for cooling the entire environment.However,facing the extreme dynamic geometry change and strain of human skin,conventional TEDs cannot align with the contour of our bodies for the best thermoregulation effect.Hence,we designed a kirigami-based wearable TED with excellent water vapor permeability,flexibility,and conformability.Numerical analysis and experimental results reveal that our product can withstand various types of large mechanical deformation without circuit rupture.The stated outcome and proposed facile approach not only reinforce the development of wearable TEDs but also offer an innovative opportunity for different electronics that require high conformability.展开更多
Implantable hydrogel-based bioelectronics(IHB)can precisely monitor human health and diagnose diseases.However,achieving biodegradability,biocompatibility,and high conformality with soft tissues poses significant chal...Implantable hydrogel-based bioelectronics(IHB)can precisely monitor human health and diagnose diseases.However,achieving biodegradability,biocompatibility,and high conformality with soft tissues poses significant challenges for IHB.Gelatin is the most suitable candidate for IHB since it is a collagen hydrolysate and a substantial part of the extracellular matrix found naturally in most tissues.This study used 3D printing ultrafine fiber networks with metamaterial design to embed into ultra-low elastic modulus hydrogel to create a novel gelatin-based conductive film(GCF)with mechanical programmability.The regulation of GCF nearly covers soft tissue mechanics,an elastic modulus from 20 to 420 kPa,and a Poisson’s ratio from-0.25 to 0.52.The negative Poisson’s ratio promotes conformality with soft tissues to improve the efficiency of biological interfaces.The GCF can monitor heartbeat signals and respiratory rate by determining cardiac deformation due to its high conformability.Notably,the gelatin characteristics of the biodegradable GCF enable the sensor to monitor and support tissue restoration.The GCF metamaterial design offers a unique idea for bioelectronics to develop implantable sensors that integrate monitoring and tissue repair and a customized method for endowing implanted sensors to be highly conformal with soft tissues.展开更多
Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduct...Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.展开更多
基金supported by the NNSF of China (12101194,11401173).
文摘In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we classify these hypersurfaces as not being of a flat affine metric.In particular,2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.
文摘In the present paper we obtain the following result: Theorem Let M^R be a compact submanifold with parallel mean curvature vector in a locally symmetric and conformally flat Riemannian manifold N^(n+p)(p>1). If then M^n lies in a totally geodesic submanifold N^(n+1).
文摘In this paper, we establish a differential equation about scalar curvature of conformally flat K-contact manifolds, and prove that a conformally symmetric K-contact manifold is a Riemann manifold with constant curvature 1. At the same time, the results on Sasaki manifolds which are given by Miyazaawa and Yamagushi are generalized to K-contact manifolds.
文摘The compact minimal submanifold in a locally symetric and conformally flat Riemann manifold is discussed in this paper.We get the Pinching constant for scalar curvature.The result of Li[2]is generallied,but the method is completely different. Meanwhile,we get better conclusion than that of [3].We also research the Pinching problem for sectional curvature on compact minimal submanifolds in a unit sphere, partially improving the results of S.T.Yan[4].
基金Supported by the National Natural Science Foundation of China.
文摘In a Robertson-Walker geometry conformally coupled to a scalar field with inflation potential V(φ)=M^(4)-(1/4)λ φ^(4),we investigate the classical evolution of a universe.The exact solutions in the model have been found.It is shown that in the region where the value of the φ field is 0<φ<φ_(max),(φ_(max) is the solution of V(φ)=0),there is inflation.This model can lead to successful inflation with λ~10^(-9),rather than 10^(-13) as previously reported.
文摘Let N n+p be an (n+p)-dimensional locally symmetric and conformally flat Riemannian manifold and Mn be an n-dimensional compact submanifold minimally immersed in N n+p . Instead of (n+p)-dimensional unit sphere, we generalize Pinching Theorems about submanifolds in unit sphere and get theorems about submanifolds in locally symmetric and conformally flat Riemannian manifold.
文摘In this paper,we extend two important theorem in[1],[2]to the minimal submanifolds in a Locally symmetric and conformally flat Riemannian mainfold N^(+p).When N^(+p)is a space S_(1)^(+p) of constant curvature,our theorems reduce to the theorems of[1],[2].
基金the National Natural Science Foundation of China(Grant No.11771099)supported by the Hong Kong Research Grant Council(Grant Nos.PolyU 15302114,15300715,15301716,15300717)supported by the Innovation Program of Shanghai Municipal Education Commission。
文摘We investigate the M-eigenvalues of the Riemann curvature tensor in the higher dimensional conformally flat manifold.The expressions of Meigenvalues and M-eigenvectors are presented in this paper.As a special case,M-eigenvalues of conformal flat Einstein manifold have also been discussed,and the conformal the invariance of M-eigentriple has been found.We also reveal the relationship between M-eigenvalue and sectional curvature of a Riemannian manifold.We prove that the M-eigenvalue can determine the Riemann curvature tensor uniquely.We also give an example to compute the Meigentriple of de Sitter spacetime which is well-known in general relativity.
文摘We review the (2 + 1)-dimensional Baňados-Teitelboim-Zanelli black hole solution in conformally invariant gravity, uplifted to (3 + 1)-dimensional spacetime. For the matter content we use a scalar-gauge field. The metric is written as <img src="Edit_be2cdfd9-fda6-4846-b64d-4d1062f9964e.bmp" alt="" /> where the <em>dilaton</em> field <span style="white-space:nowrap;"><span style="white-space:nowrap;">ω</span></span> contains all the scale dependencies and where <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" /> represents the “un-physical” spacetime. A numerical solution is presented and shows how the dilaton can be treated on equal footing with the scalar field. The location of the apparent horizon and ergo-surface depends critically on the parameters and initial values of the model. It is not a hard task to find suitable initial parameters in order to obtain a regular and singular free <img src="Edit_5d830100-019b-4a6a-82e7-deefdf327ecc.bmp" alt="" /> out of a BTZ-type solution for <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" style="white-space:normal;" />. In the vacuum situation, an exact time-dependent solution in the Eddington-Finkelstein coordinates is found, which is valid for the (2 + 1)-dimensional BTZ spacetime as well as for the uplifted (3 + 1)-dimensional BTZ spacetime. While <img src="Edit_ffd065ec-fc7e-41cd-b2c6-05b86c3b566a.bmp" alt="" style="white-space:normal;" /> resembles the standard BTZ solution with its horizons, <img src="Edit_5d830100-019b-4a6a-82e7-deefdf327ecc.bmp" alt="" style="white-space:normal;" /> is flat. The dilaton field becomes an infinitesimal renormalizable quantum field, which switches on and off Hawking radiation. This solution can be used to investigate the small distance scale of the model and the black hole complementarity issues. It can also be used to describe the problem of how to map the quantum states of the outgoing radiation as seen by a distant observer and the ingoing by a local observer in a one-to-one way. The two observers will use a different conformal gauge. A possible connection is made with the antipodal identification and unitarity issues. This research shows the power of conformally invariant gravity and can be applied to bridge the gap between general relativity and quantum field theory in the vicinity of the horizons of black holes.
基金DST,New Delhi,India,for its financial support for research facilities under DSTFIST-2019。
文摘This paper investigates wormhole solutions within the framework of extended symmetric teleparallel gravity,incorporating non-commutative geometry,and conformal symmetries.To achieve this,we examine the linear wormhole model with anisotropic fluid under Gaussian and Lorentzian distributions.The primary objective is to derive wormhole solutions while considering the influence of the shape function on model parameters under Gaussian and Lorentzian distributions.The resulting shape function satisfies all the necessary conditions for a traversable wormhole.Furthermore,we analyze the characteristics of the energy conditions and provide a detailed graphical discussion of the matter contents via energy conditions.Additionally,we explore the effect of anisotropy under Gaussian and Lorentzian distributions.Finally,we present our conclusions based on the obtained results.
基金This work is financially supported by the National Natural Science Foundation of China(52303036)the Natural Science Foundation of Guangxi Province(2020GXNSFAA297028)+4 种基金the Guangxi Science and Technology Base and Talent Special Project(GUIKE AD23026179)the International Science&Technology Cooperation Project of Chengdu(2021-GH03-00009-HZ)the Program of Innovative Research Team for Young Scientists of Sichuan Province(22CXTD0019)the Natural Science Foundation of Sichuan Province(2023NSFSC0986)the Opening Project of State Key Laboratory of Polymer Materials Engineering(Sichuan University)(Sklpme2023-3-18).
文摘Electromagnetic interference shielding(EMI SE)modules are the core com-ponent of modern electronics.However,the tra-ditional metal-based SE modules always take up indispensable three-dimensional space inside electronics,posing a major obstacle to the integra-tion of electronics.The innovation of integrating 3D-printed conformal shielding(c-SE)modules with packaging materials onto core electronics offers infinite possibilities to satisfy ideal SE func-tion without occupying additional space.Herein,the 3D printable carbon-based inks with various proportions of graphene and carbon nanotube nanoparticles are well-formulated by manipulating their rheological peculiarity.Accordingly,the free-constructed architectures with arbitrarily-customized structure and multifunctionality are created via 3D printing.In particular,the SE performance of 3D-printed frame is up to 61.4 dB,simultaneously accompanied with an ultralight architecture of 0.076 g cm^(-3) and a superhigh specific shielding of 802.4 dB cm3 g^(-1).Moreover,as a proof-of-concept,the 3D-printed c-SE module is in situ integrated into core electronics,successfully replacing the traditional metal-based module to afford multiple functions for electromagnetic compatibility and thermal dissipa-tion.Thus,this scientific innovation completely makes up the blank for assembling carbon-based c-SE modules and sheds a brilliant light on developing the next generation of high-performance shielding materials with arbitrarily-customized structure for integrated electronics.
基金supported by the National Natural Science Foundation of China(No.62122002)the Project of City University of Hong Kong(Nos.9667221,9678274,and 9680322)+1 种基金as part of the InnoHK Project on Project 2.2—AI-based 3D ultrasound imaging algorithm at Hong Kong Centre for Cerebro-Cardiovascular Health Engineering(COCHE)the Project of Research Grants Council of the Hong Kong Special Administrative Region(Nos.11213721,11215722,and 11211523)。
文摘The application of thermoelectric devices(TEDs)for personalized thermoregulation is attractive for saving energy while balancing the quality of life.TEDs that directly attach to human skin remarkably minimized the energy wasted for cooling the entire environment.However,facing the extreme dynamic geometry change and strain of human skin,conventional TEDs cannot align with the contour of our bodies for the best thermoregulation effect.Hence,we designed a kirigami-based wearable TED with excellent water vapor permeability,flexibility,and conformability.Numerical analysis and experimental results reveal that our product can withstand various types of large mechanical deformation without circuit rupture.The stated outcome and proposed facile approach not only reinforce the development of wearable TEDs but also offer an innovative opportunity for different electronics that require high conformability.
基金This work was sponsored by the National Natural Science Foundation of China(No.52235007,52325504)the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(No.T2121004).
文摘Implantable hydrogel-based bioelectronics(IHB)can precisely monitor human health and diagnose diseases.However,achieving biodegradability,biocompatibility,and high conformality with soft tissues poses significant challenges for IHB.Gelatin is the most suitable candidate for IHB since it is a collagen hydrolysate and a substantial part of the extracellular matrix found naturally in most tissues.This study used 3D printing ultrafine fiber networks with metamaterial design to embed into ultra-low elastic modulus hydrogel to create a novel gelatin-based conductive film(GCF)with mechanical programmability.The regulation of GCF nearly covers soft tissue mechanics,an elastic modulus from 20 to 420 kPa,and a Poisson’s ratio from-0.25 to 0.52.The negative Poisson’s ratio promotes conformality with soft tissues to improve the efficiency of biological interfaces.The GCF can monitor heartbeat signals and respiratory rate by determining cardiac deformation due to its high conformability.Notably,the gelatin characteristics of the biodegradable GCF enable the sensor to monitor and support tissue restoration.The GCF metamaterial design offers a unique idea for bioelectronics to develop implantable sensors that integrate monitoring and tissue repair and a customized method for endowing implanted sensors to be highly conformal with soft tissues.
基金National Natural Science Foundation of China(Nos.42071444,42101444)。
文摘Cultural relics line graphic serves as a crucial form of traditional artifact information documentation,which is a simple and intuitive product with low cost of displaying compared with 3D models.Dimensionality reduction is undoubtedly necessary for line drawings.However,most existing methods for artifact drawing rely on the principles of orthographic projection that always cannot avoid angle occlusion and data overlapping while the surface of cultural relics is complex.Therefore,conformal mapping was introduced as a dimensionality reduction way to compensate for the limitation of orthographic projection.Based on the given criteria for assessing surface complexity,this paper proposed a three-dimensional feature guideline extraction method for complex cultural relic surfaces.A 2D and 3D combined factor that measured the importance of points on describing surface features,vertex weight,was designed.Then the selection threshold for feature guideline extraction was determined based on the differences between vertex weight and shape index distributions.The feasibility and stability were verified through experiments conducted on real cultural relic surface data.Results demonstrated the ability of the method to address the challenges associated with the automatic generation of line drawings for complex surfaces.The extraction method and the obtained results will be useful for line graphic drawing,displaying and propaganda of cultural relics.
