Some Topics on Complex Finsler Manifold

复$Finsler$流形是具有复$Finsler$度量的复流形，它是$Hermitian$流形的推广。复流形上著名的$Kobayshi$度量和$Carath\acute{e}odory$度量（不一定光滑）都是复$Finsler$度量。本文以具光滑$Finsler$度量的复流形为研究对象。讨论了复$Finsler$度量的射影等价关系、对$Cartan$联络与$Chern-Finsler$联络进行比较，并对一类重要的复$Finsler$度量----$Randers$度量进行讨论。全文共分四章,其中第二章和第四章都是将实的情形推广到复流形中,第三章为$Cartan$联络与$Chern-Finsler...Complex Finsler manifold is a manifold endowed with Complex Finsler metrics. It is the generalization of the usual Hermitian manifold. It is well known, that the Kobayshi metric and the Carath$\acute{e}$odory metric (not necessarily smooth) are the famous Finsler metrics on the Complex manifold. In this paper , we do the research on the complex manifold endowed with smooth Finsler metrics, study ...学位：理学硕士院系专业：数学科学学院数学系_基础数学学号：S20032301

Bochner technique on complex Finsler manifolds

“{\largeBochner}技巧”一词是描述由{\largeS.Bochner}首创的一种方法([1-2])．六十多年前，{\largeBochner}用这一技巧证明：在{\largeRicci}曲率满足一定的条件下，{\largeRiemann}流形上某些几何上有兴趣的对象(例如{\largeKilling}向量场、调和形式、旋量场)必定平行或者为零．今天，{\largeBochner}技巧已成为几何学者们的基本术语之一，并得到了广泛的应用．近些年来，由于{\largeFinsler}流形上的{\largeLaplace}算子理论已取得了许多重要的进展([34][24][11][14-1...{\large The term “Bochner technique” describes a method initiated by S.Bochner([1-2]). Sixty years ago, Bochner used this method to prove that certain objects of geometric interest(e.g.Killing vector fields, harmonic forms, harmonic spinor fields,etc) on compact Riemannian manifolds under certain suitable condition of Ricci curvature must be parallel or vanished identically.Today, the “Bochner tec...学位：理学博士院系专业：数学科学学院数学与应用数学系_基础数学学号：1902006015315

复Finsler流形上的两个问题

类似于实Finsler流形,在复流形的全纯切丛上引进Finsler度量F,并且定义G=F2为垂直丛上一Hermitian度量,然后利用Hermitian一些技巧得到复Finsler流形上的一些几何性质.在此基础上讨论了复流形M上给定的两个弱Kahler复Finsler度量,如果它们射影等价则必仿射等价,以及流形M上赋予由复Berwald流形上复Finsler度量诱导的实Finsler度量必为实Berwald流形

一类乘积域的全纯自同构群

设Bn为n维复单位球,Um为m维多圆柱.本文利用全纯自同构将边界映为边界的这一性质,得到了乘积域Bn×Um的全纯自同构的一些必要条件,再从这些必要条件出发,成功找到了乘积域Bn×Um的全部全纯自同构.在总的思路上,本篇文章采用的是类似于得到单复变中单位圆盘的Aut(U)的方法,即把零点映为零点的全纯自同构(类似于单复变函数论中的旋转变换)与一类特殊的全纯自同构(类似于单复变函数论中的M bius变换)复合

BOCHNER TECHNIQUE ON STRONG KHLER-FINSLER MANIFOLDS

By using the Chern-Finsler connection and complex Finsler metric,the Bochner technique on strong Khler-Finsler manifolds is studied.For a strong Khler-Finsler manifold M,the authors first prove that there exists a system of local coordinate which is normalized at a point v ∈ M-=T 1,0M\o(M),and then the horizontal Laplace operator H for diffierential 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 diffierential forms on PTM.Moreover,the Bochner vanishing theorem on a holomorphic line bundle over PTM is also obtaine

B_2×B_2的全纯自同构群

讨论B2×B2上的全纯自同构群,并计算它的B ergm an核函数及其自同构的Jacob i行列式

Holomorphic automorphism group of B2×B 2

摘　要　讨论B2×B2 上的全纯自同构群, 并计算它的Bergman 核函数及其自同构的Jacobi 行 列式. Abstract　In th is paper w e first investigate the holomorph ic automorph ism group of B 2×B 2, then calculate the Bergman kernel and the Jacobi determ inant of the automorph ism of B 2×B 2.国家自然科学基金(10501036; 10271097) ; 福建省自然科学基金资助项目(J 0511003

复Finsler流形间的调和映射

通过定义其上的整体内积得到相应的伴随算子和Laplace算子,并且通过计算得到了强拟凸复Finsler流形间光滑映射的-能量和-能量的变分公式,从而给出了调和映射的定义;最后得到-量与-量之差不是同伦不变的