In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and local...In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and locally conformal pseudo-Kahler Finsler manifold,which is simply connected or whose fundamental group contains elements of nite order only,can be given a Kahler metric.展开更多
This article generalizes the formulas of Gauss-Ostrogradskii type for semibasic vector fields from Riemannian manifolds to real Finsler manifolds and obtains some formulas of Gauss-Ostrogradskii type for Finsler vecto...This article generalizes the formulas of Gauss-Ostrogradskii type for semibasic vector fields from Riemannian manifolds to real Finsler manifolds and obtains some formulas of Gauss-Ostrogradskii type for Finsler vector fields which are expressed in terms of the vertical and horizontal derivatives of the Cartan connection in real Finsler manifolds.展开更多
Let （M1, F1） and （M2, F2） be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold （f2 M1 x h M2, F） of （M1, F1） and （M2, F2） is the product manifold M1 x ...Let （M1, F1） and （M2, F2） be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold （f2 M1 x h M2, F） of （M1, F1） and （M2, F2） is the product manifold M1 x M2 endowed with the warped product complex 2 2 Finsler metric F2 = f2F1 ＋ fl F2, where fl and f2 are positive smooth functions on M1 and M2, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be K/ihler Finsler （resp., weakly K/ihler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg） manifold are ob- tained, respectively. It is proved that if （M1, F1） and （M2,F2） are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if fl and f2 are positive constants.展开更多
Let （M, F ） be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds （M 1 , F 1 ） and （M 2 , F 2 ）. In this paper, we obtain the relationship between the Chern Finsler conne...Let （M, F ） be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds （M 1 , F 1 ） and （M 2 , F 2 ）. In this paper, we obtain the relationship between the Chern Finsler connection coefficients Γ i ; k associated to F and the Chern Finsler connection coefficients Γ a ; c , Γα ; γ associated to F 1 , F 2 , respectively. As applications we prove that, if both （M 1 , F 1 ） and （M 2 , F 2 ） are strongly Ka¨hler Finsler （complex Berwald, or locally complex Minkowski, respectively） manifolds, so does （M, F ）. Furthermore, we prove that the holomorphic curvature K F = 0 if and only if K F1 = 0 and K F2 = 0.展开更多
A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the ...A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E.展开更多
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
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.
In this article, we study a class of Finsler metrics called general （α, β）-metrics, which are defined by a Riemannian metric α and a 1-form β. We determine all of Douglas general （α, β）-metrics on a manifold...In this article, we study a class of Finsler metrics called general （α, β）-metrics, which are defined by a Riemannian metric α and a 1-form β. We determine all of Douglas general （α, β）-metrics on a manifold of dimension n 〉 2.展开更多
By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong K/ihler-Finsler manifolds is studied. For a strong K/ihler-Finsler manifold M, the authors first prove that there exist...By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong K/ihler-Finsler manifolds is studied. For a strong K/ihler-Finsler manifold M, the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈M = T1.0M／o（M）, and then the horizontal Laplace operator NH for differential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor, and the horizontal Laplace operator H on holomorphic vector bundle over PTM is also defined. Finally, we get a Bochner vanishing theorem for differential forms on PTM. Moreover, the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtained展开更多
In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound es...In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.12001165)Postdoctoral Research Foundation of China(Grant No.2019M652513)Postdoctoral Research Foundation of Henan Province(Grant No.19030050).
文摘In this paper,we give a necessary and sucient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal pseudo-Kahler Finsler.As an application,we nd any complete strongly convex and locally conformal pseudo-Kahler Finsler manifold,which is simply connected or whose fundamental group contains elements of nite order only,can be given a Kahler metric.
基金Program for New Century Excellent Talents in Fujian Province Universitythe Natural Science Foundation of China(10601040,10571144)+1 种基金the Tian Yuan Foundation of China(10526033)China Postdoctoral Science Foundation(2005038639)
文摘This article generalizes the formulas of Gauss-Ostrogradskii type for semibasic vector fields from Riemannian manifolds to real Finsler manifolds and obtains some formulas of Gauss-Ostrogradskii type for Finsler vector fields which are expressed in terms of the vertical and horizontal derivatives of the Cartan connection in real Finsler manifolds.
基金supported by Program for New Century Excellent Talents in University(NCET-13-0510)National Natural Science Foundation of China(11271304,11571288,11461064)+1 种基金the Fujian Province Natural Science Funds for Distinguished Young Scholar(2013J06001)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘Let （M1, F1） and （M2, F2） be two strongly pseudoconvex complex Finsler man- ifolds. The doubly wraped product complex Finsler manifold （f2 M1 x h M2, F） of （M1, F1） and （M2, F2） is the product manifold M1 x M2 endowed with the warped product complex 2 2 Finsler metric F2 = f2F1 ＋ fl F2, where fl and f2 are positive smooth functions on M1 and M2, respectively. In this paper, the most often used complex Finsler connections, holomorphic curvature, Ricci scalar curvature, and real geodesics of the DWP-complex Finsler manifold are derived in terms of the corresponding objects of its components. Necessary and sufficient conditions for the DWP-complex Finsler manifold to be K/ihler Finsler （resp., weakly K/ihler Finsler, complex Berwald, weakly complex Berwald, complex Landsberg） manifold are ob- tained, respectively. It is proved that if （M1, F1） and （M2,F2） are projectively flat, then the DWP-complex Finsler manifold is projectively flat if and only if fl and f2 are positive constants.
基金supported by Program for New Century Excellent Talents in Fujian Provincial Universitythe Natural Science Foundation of China (10971170 10601040)
文摘Let （M, F ） be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds （M 1 , F 1 ） and （M 2 , F 2 ）. In this paper, we obtain the relationship between the Chern Finsler connection coefficients Γ i ; k associated to F and the Chern Finsler connection coefficients Γ a ; c , Γα ; γ associated to F 1 , F 2 , respectively. As applications we prove that, if both （M 1 , F 1 ） and （M 2 , F 2 ） are strongly Ka¨hler Finsler （complex Berwald, or locally complex Minkowski, respectively） manifolds, so does （M, F ）. Furthermore, we prove that the holomorphic curvature K F = 0 if and only if K F1 = 0 and K F2 = 0.
基金supported by Tian Yuan Foundation of China (10526033)China Postdoctoral Science Foundation (2005038639)the Natural Science Foundation of China (10601040,10571144).
文摘A vector bundle F over the tangent bundle TM of a manifold M is said to be a Finsler vector bundle if it is isomorphic to the pull-back π^＊E of a vector bundle E over M（[1]）. In this article the authors study the h-Laplace operator in Finsler vector bundles. An h-Laplace operator is defined, first for functions and then for horizontal Finsler forms on E. Using the h-Laplace operator, the authors define the h-harmonic function and ho harmonic horizontal Finsler vector fields, and furthermore prove some integral formulas for the h-Laplace operator, horizontal Finsler vector fields, and scalar fields on E.
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.
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supported by the National Natural Science Foundation of China(11626091)Youth Science Fund of Henan Normal University(2015QK01)a doctoral scientific research foundation of Henan Normal University(5101019170130)
文摘In this article, we study a class of Finsler metrics called general （α, β）-metrics, which are defined by a Riemannian metric α and a 1-form β. We determine all of Douglas general （α, β）-metrics on a manifold of dimension n 〉 2.
基金Supported by the National Natural Science Foundation of China (10571144,10771174)Program for New Centery Excellent Talents in Xiamen University
文摘By using the Chern-Finsler connection and complex Finsler metric, the Bochner technique on strong K/ihler-Finsler manifolds is studied. For a strong K/ihler-Finsler manifold M, the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈M = T1.0M／o（M）, and then the horizontal Laplace operator NH for differential forms on PTM is defined by the horizontal part of the Chern-Finsler connection and its curvature tensor, and the horizontal Laplace operator H on holomorphic vector bundle over PTM is also defined. Finally, we get a Bochner vanishing theorem for differential forms on PTM. Moreover, the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtained
文摘In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry.
