In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold ...In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.展开更多
In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
Let X be a compact K?hler manifold and D be a simple normal crossing divisor. If D is the support of some effective q-ample divisor, we show H^i(X, ?_X^j (log D)) = 0, for i + j > n + q.
Using non-linear connection of Finsler manifold M, the existence of local coordinates which is normalized at a point x is proved, and the Laplace operator A on 1-form of M is defined by non-linear connection and its c...Using non-linear connection of Finsler manifold M, the existence of local coordinates which is normalized at a point x is proved, and the Laplace operator A on 1-form of M is defined by non-linear connection and its curvature tensor. After proving the maximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theorem of Killing vectors and harmonic 1-form are obtained.展开更多
In this paper,we consider the d-boundedness of the Bergman metric and a vanishing theorem of L2-cohomology on a class of Hartogs domain,whose base domain is the production of two irreducible bounded symmetric domains ...In this paper,we consider the d-boundedness of the Bergman metric and a vanishing theorem of L2-cohomology on a class of Hartogs domain,whose base domain is the production of two irreducible bounded symmetric domains of the first type,by using the Bergman kernel function,invariant function,holomorphic automorphism group and so on.展开更多
We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0（2, 2）/SO（2） × SO（2）. Let π ： E →＊ M be any vector bundle. Then ...We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0（2, 2）/SO（2） × SO（2）. Let π ： E →＊ M be any vector bundle. Then any E-valued L2 harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.展开更多
We generalize the logarithmic decomposition theorem of Deligne–Illusie to a filtered version.There are two applications.The easier one provides a mod p proof for a vanishing theorem in characteristic zero.The deeper ...We generalize the logarithmic decomposition theorem of Deligne–Illusie to a filtered version.There are two applications.The easier one provides a mod p proof for a vanishing theorem in characteristic zero.The deeper one gives rise to a positive characteristic analogue of a theorem of Deligne on the mixed Hodge structure attached to complex algebraic varieties.展开更多
Let M be a connected complex manifold endowed with a Hermitian metric g.In this paper,the complex horizontal and vertical Laplacians associated with the induced Hermitian metric <·,·>on the holomorphic...Let M be a connected complex manifold endowed with a Hermitian metric g.In this paper,the complex horizontal and vertical Laplacians associated with the induced Hermitian metric <·,·>on the holomorphic tangent bundle T 1,0M of M are defined,and their explicit expressions are obtained.Using the complex horizontal and vertical Laplacians associated with the Hermitian metric <·,·>on T 1,0M,we obtain a vanishing theorem of holomorphic horizontal p forms which are compactly supported in T 1,0M under the condition that g is a Kaehler metric on M.展开更多
We here study the Brill-Noether theory for rank two vector bundles generated by their sections. We generalize the vanishing theorem, the Clifford theorem and the existence theorem to such bundles.
We introduce two Hopf algebroids associated to a proper and holomorphic Lie group action on a complex manifold. We prove that the cyclic cohomology of each Hopf algebroid is equal to the Dolbeault cohomology of invari...We introduce two Hopf algebroids associated to a proper and holomorphic Lie group action on a complex manifold. We prove that the cyclic cohomology of each Hopf algebroid is equal to the Dolbeault cohomology of invariant differential forms. When the action is cocompact, we develop a generalized complex Hodge theory for the Dolbeault cohomology of invariant differential forms. We prove that every cyclic cohomology class of these two Hopf algebroids can be represented by a generalized harmonic form. This implies that the space of cyclic cohomology of each Hopf algebroid is finite dimensional. As an application of the techniques developed in this paper, we generalize the Serre duality and prove a Kodaira type vanishing theorem.展开更多
In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed＇s odd dimensional index formula. Then we extend this theorem to the noncommuta- tive geometry framework. As a c...In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed＇s odd dimensional index formula. Then we extend this theorem to the noncommuta- tive geometry framework. As a corollary, we get the odd family Lichnerowicz vanishing theorem and the odd family Atiyah-Hirzebruch vanishing theorem.展开更多
文摘In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms.
基金supported by National Natural Science Foundation of USA(Grant No.DMS0705284)National Natural Science Foundation of China(Grant No.10801027)
文摘In this paper,we compute the adiabatic limit of the scalar curvature and prove several vanishing theorems by taking adiabatic limits.As an application,we give a Kastler-Kalau-Walze type theorem for foliations.
文摘Let X be a compact K?hler manifold and D be a simple normal crossing divisor. If D is the support of some effective q-ample divisor, we show H^i(X, ?_X^j (log D)) = 0, for i + j > n + q.
基金Project supported by the Natural Science Foundation of China(10271097)
文摘Using non-linear connection of Finsler manifold M, the existence of local coordinates which is normalized at a point x is proved, and the Laplace operator A on 1-form of M is defined by non-linear connection and its curvature tensor. After proving the maximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theorem of Killing vectors and harmonic 1-form are obtained.
基金Supported by National Natural Science Foundation of China(Grant No.11871044)Natural Science Foundation of Hebei Province(Grant No.A201906037)。
文摘In this paper,we consider the d-boundedness of the Bergman metric and a vanishing theorem of L2-cohomology on a class of Hartogs domain,whose base domain is the production of two irreducible bounded symmetric domains of the first type,by using the Bergman kernel function,invariant function,holomorphic automorphism group and so on.
文摘We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0（2, 2）/SO（2） × SO（2）. Let π ： E →＊ M be any vector bundle. Then any E-valued L2 harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.
文摘We generalize the logarithmic decomposition theorem of Deligne–Illusie to a filtered version.There are two applications.The easier one provides a mod p proof for a vanishing theorem in characteristic zero.The deeper one gives rise to a positive characteristic analogue of a theorem of Deligne on the mixed Hodge structure attached to complex algebraic varieties.
基金supported by the Program for New Century Excellent Talents in Fujian Province and National Natural Science Foundation of China(Grant Nos.10601040,10971170)
文摘Let M be a connected complex manifold endowed with a Hermitian metric g.In this paper,the complex horizontal and vertical Laplacians associated with the induced Hermitian metric <·,·>on the holomorphic tangent bundle T 1,0M of M are defined,and their explicit expressions are obtained.Using the complex horizontal and vertical Laplacians associated with the Hermitian metric <·,·>on T 1,0M,we obtain a vanishing theorem of holomorphic horizontal p forms which are compactly supported in T 1,0M under the condition that g is a Kaehler metric on M.
文摘We here study the Brill-Noether theory for rank two vector bundles generated by their sections. We generalize the vanishing theorem, the Clifford theorem and the existence theorem to such bundles.
文摘We introduce two Hopf algebroids associated to a proper and holomorphic Lie group action on a complex manifold. We prove that the cyclic cohomology of each Hopf algebroid is equal to the Dolbeault cohomology of invariant differential forms. When the action is cocompact, we develop a generalized complex Hodge theory for the Dolbeault cohomology of invariant differential forms. We prove that every cyclic cohomology class of these two Hopf algebroids can be represented by a generalized harmonic form. This implies that the space of cyclic cohomology of each Hopf algebroid is finite dimensional. As an application of the techniques developed in this paper, we generalize the Serre duality and prove a Kodaira type vanishing theorem.
基金Supported by National Natural Science Foundation of China(Grant No.11271062)Program for New Century Excellent Talents in University(Grant No.13-0721)
文摘In this paper, we prove a local odd dimensional equivariant family index theorem which generalizes Freed＇s odd dimensional index formula. Then we extend this theorem to the noncommuta- tive geometry framework. As a corollary, we get the odd family Lichnerowicz vanishing theorem and the odd family Atiyah-Hirzebruch vanishing theorem.
