This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the author...This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds.展开更多
Y-Riemannian metric gY is an important tool in Finsler geometry, where Y is a smooth non-zero vector field on Finsler manifold. If Y is a geodesic field, it is very effective to study flag curvature using Y-Riemann me...Y-Riemannian metric gY is an important tool in Finsler geometry, where Y is a smooth non-zero vector field on Finsler manifold. If Y is a geodesic field, it is very effective to study flag curvature using Y-Riemann metric. In this paper, using a special Y-Riemann metric ( that is, so called v-Riemann metric ), we study hyperspheres in a Minkowski space and give some characteristics of hyperspheres in a Minkowski space.展开更多
In this paper, the Kahler conditions of the Chern-Finsler connection in complex Finsler geometry are studied, and it is proved that Kahler Finsler metrics are actually strongly Kahler.
By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation the...By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.展开更多
Using the invariant integral kernel introduced by Demailly and Laurent-Thiebaut, complex Finsler metric and nonlinear connection associating with Chern-Finsler connection, we research the integral representation theor...Using the invariant integral kernel introduced by Demailly and Laurent-Thiebaut, complex Finsler metric and nonlinear connection associating with Chern-Finsler connection, we research the integral representation theory on complex Finsler manifolds. The Koppelman and Koppelman-Leray formulas are obtained, and the \(\overline \partial \)-equations are solved.展开更多
Let （E, F） be a complex Finsler vector bundle over a compact Kahler manifold （M, g） with Kahler form φ We prove that if （E, F） is a weakly complex Einstein-Finsler vector bundle in the sense of Aikou （1997）, ...Let （E, F） be a complex Finsler vector bundle over a compact Kahler manifold （M, g） with Kahler form φ We prove that if （E, F） is a weakly complex Einstein-Finsler vector bundle in the sense of Aikou （1997）, then it is modeled on a complex Minkowski space. Consequently, a complex Einstein-Finsler vector bundle （E, F） over a compact Kahler manifold （M, g） is necessarily φ-semistable and （E,F）=（E1,F1）……（Ek,Fk）,where Fj ：= F｜Ej, and each （Ej, Fj） is modeled on a complex Minkowski space whose associated Hermitian vector bundle is a φ-stable Einstein-Hermitian vector bundle with the same factor c as （E, F）.展开更多
The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically. Furthermore, an interesting open problem has been proposed in this field.
文摘This paper studies the induced Chern connection of submanifolds in a Finsler manifold and gets the relations between the induced Chern connection and the Chern connection of the induced Finsler metric. Then the authors point out a difference between Finsler submanifolds and Riemann submanifolds.
基金Supported by the National Natural Science Foundation of China(10171117) and the Science Foundation of Chongqing Education Committee.
文摘Y-Riemannian metric gY is an important tool in Finsler geometry, where Y is a smooth non-zero vector field on Finsler manifold. If Y is a geodesic field, it is very effective to study flag curvature using Y-Riemann metric. In this paper, using a special Y-Riemann metric ( that is, so called v-Riemann metric ), we study hyperspheres in a Minkowski space and give some characteristics of hyperspheres in a Minkowski space.
基金Project supported by the National Natural Science Foundation of China (No. 10571154)
文摘In this paper, the Kahler conditions of the Chern-Finsler connection in complex Finsler geometry are studied, and it is proved that Kahler Finsler metrics are actually strongly Kahler.
基金This work was supported by the National Natural Science Foundation of China and China Postdoctoral Science Foundation(Grant No.10271097,20040350105)Program for New Century Excellent Talents in Xiamen University.
文摘By means of the invariant integral kernel (the Berndtsson kernel), the complex Finsler metric and the non-linear connection associated with the Chern-Finsler connection to research into the integral representation theory on complex Finsler manifolds, theKoppelman and Koppelman-Leray formulas are obtained, and the - -equations are solved.
基金This work was supported by the National Natural Science Foundation and Mathematical Tianyuan Foundation of China and the Natural Science Foundation of Fujian(Grant No.10271097,TY10126033,F0110012).
文摘Using the invariant integral kernel introduced by Demailly and Laurent-Thiebaut, complex Finsler metric and nonlinear connection associating with Chern-Finsler connection, we research the integral representation theory on complex Finsler manifolds. The Koppelman and Koppelman-Leray formulas are obtained, and the \(\overline \partial \)-equations are solved.
基金supported by National Natural Science Foundation of China(Grant Nos.11671330 and 11271304)the Fujian Province Natural Science Funds for Distinguished Young Scholar(Grant No.2013J06001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘Let （E, F） be a complex Finsler vector bundle over a compact Kahler manifold （M, g） with Kahler form φ We prove that if （E, F） is a weakly complex Einstein-Finsler vector bundle in the sense of Aikou （1997）, then it is modeled on a complex Minkowski space. Consequently, a complex Einstein-Finsler vector bundle （E, F） over a compact Kahler manifold （M, g） is necessarily φ-semistable and （E,F）=（E1,F1）……（Ek,Fk）,where Fj ：= F｜Ej, and each （Ej, Fj） is modeled on a complex Minkowski space whose associated Hermitian vector bundle is a φ-stable Einstein-Hermitian vector bundle with the same factor c as （E, F）.
文摘The history of Finsler geometry is reviewed and briefly recent development in Finsler geometry and its application is completed systematically. Furthermore, an interesting open problem has been proposed in this field.
