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
We introduce a fundamental connection in Finsler geometry,which is torsion-free and almost compatible with the induced metric. We give the difference between this connection and other known connections.
By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a Stein manifold, and un...By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of δ^--equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of δ^--equation for （p, q） differential forms on a Stein manifold.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, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q whi...In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q which are both belong to C s+α p,q-1 (D) and ob tain integral representation of the solution of (p,q)-form b-equation on the boundary of pseudoconvex domain in Stein manifolds and the L s p,q extimates for the solution.展开更多
In this paper, the Laplacian on the holomorphic tangent bundle T 1,0 M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using th...In this paper, the Laplacian on the holomorphic tangent bundle T 1,0 M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M, F ). Utilizing the initiated "Bochner technique", a vanishing theorem for vector fields on the holomorphic tangent bundle T 1,0 M is obtained.展开更多
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.
文摘We introduce a fundamental connection in Finsler geometry,which is torsion-free and almost compatible with the induced metric. We give the difference between this connection and other known connections.
基金the National Natural Science Foundation of China(10571144,10771174,10601,040)Program for New Century Excellent Talents in Xiamen University
文摘By means of the Hermitian metric and Chern connection, Qiu [4] obtained the Koppelman-Leray-Norguet formula for （p, q） differential forms on an open set with C^1 piecewise smooth boundary on a Stein manifold, and under suitable conditions gave the solutions of δ^--equation on a Stein manifold. In this article, using the method of Range and Siu [5], under suitable conditions, the authors complicatedly calculate to give the uniform estimates of solutions of δ^--equation for （p, q） differential forms on a Stein manifold.
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.
文摘In this paper, by using holomorphic support f unction of strictly pseudoconvex domain on Stein manifolds and the kernel define d by DEMAILY J P and Laurent Thiebaut, we construct two integral operators T q and S q which are both belong to C s+α p,q-1 (D) and ob tain integral representation of the solution of (p,q)-form b-equation on the boundary of pseudoconvex domain in Stein manifolds and the L s p,q extimates for the solution.
基金Project Supported by the National Natural Science Foundation of China (Nos. 10871145, 10771174)the Doctoral Program Foundation of the Ministry of Education of China (No. 2009007Q110053)
文摘In this paper, the Laplacian on the holomorphic tangent bundle T 1,0 M of a complex manifold M endowed with a strongly pseudoconvex complex Finsler metric is defined and its explicit expression is obtained by using the Chern Finsler connection associated with (M, F ). Utilizing the initiated "Bochner technique", a vanishing theorem for vector fields on the holomorphic tangent bundle T 1,0 M is obtained.
