Hermitian调和映照的Schwarz引理

由Jost和Yau引进的Hermitian调和映照是Riemannian流形上通常的调和映照在Hermitian流形上的一种自然的类比.本文证明了复分析中经典的Schwarz引理对一大类Hermitian调和映照仍然成立.作为推论,我们得到了半共形Hermitian调和映照的Liouville性质.     

双扭曲积Hermitian流形

主要研究双扭曲积Hermitian流形的各种曲率,给出了紧致非平凡的双扭曲积Hermitian流形具有常全纯截面曲率的充要条件,得到了一种构造满足第一或第二爱因斯坦条件的Hermitian流形的有效方法.     

实双截曲率、Miyaoka-Yau不等式和K?hler-Ricci流（英文）

为了把Wu-Yau理论([Invent. Math.,2016,204(2):595-604])推广到Hermitian情形,在文献[Trans.Amer. Math. Soc.,2019,371(4):2703-2718]中,杨晓奎和郑方阳在Hermitian流形上引进了实双截曲率的概念.本文证明:如果(X,h)是一个有非正实双截曲率的紧Hermitian流形,并且义上面还存在一个Kahler度量,那么Miyaoka-Yau不等式成立.另外,当Hermitian度量的实双截曲率有正的上界时,我们能给出Kahler-Ricci流的解的存在区间估计.     

乘积复流形上的Szabó度量

设(M_1,α),(M_2,β)均为Hermitian流形,本文证明了积流形M_1×M_2上的复Szabó度量F_ε是Berwald度量,且当α,β为K(?)hler度量时,F_ε是强Kahler-Finsler度量,此外本文还给出了F_ε的全纯曲率的显式表达式．     

乘积复流形上的Szabó度量

设(M_1,α),(M_2,β)均为Hermitian流形,本文证明了积流形M_1×M_2上的复Szabó度量F_ε是Berwald度量,且当α,β为K(?)hler度量时,F_ε是强Kahler-Finsler度量,此外本文还给出了F_ε的全纯曲率的显式表达式．     

近凯勒流形中一般子流形的淹没

本文讨论了近凯勒(nearly K(a|¨)hler)流形中一般子流形的淹没,证明了:如果π:M→B是近凯勒流形M中子流形M到殆埃尔米特(almost Hermitian)流形B的淹没,那么B是近凯勒流形.另外,本文给出了关于这种淹没分解理论的一些性质,并且研究了M和B的全纯截面曲率之间的关系.     

关于减小体积的调和映射

1.二个同维数的光滑流形之间,映射的体积元之比是映射的最简单、最重要的度量不变量。陈省身教授[1]讨论了同维数 Hermitian 流形间和乐映射的减小体积性质,推广了著名的 Schwarz 引理,陈省身和 Goldberg[2]又对同维数实黎曼流形间的调和映射作了研究,得到若干减小体积的定理。本文将考虑二个不同维数的黎曼流形间的调和映射,以便推广[2]中有关的结论。     

Khler流形上的Gilkey定理

在本文中,我们证明下列结果:设ω(g,h)是紧致复n维Khler流形M上由Khler度量g和M上Hermitian矢丛E的Hermitian结构h所确定的值为M上(p,q)型微分形式的r阶不变多项式函数,则当r相似文献   

共形复Finsler流形上的交换公式

设M为n维复流形,M^-～=T~（1,0）M-{0},F为M上的强拟凸复Finsler度量, F^-=e^σF为F的共形变换。本文得到定义在M^-上的各种Hermitian张量场分别关于复Finsler流形（M,F）和（M,F^-）的复Rund联络求共变微分的各种交换公式。     

特征2的除环上Hermitian矩阵几何

设D 是带对合的除环. 当char(D) ≠ 2 时, D 上Hermitian 矩阵几何的基本定理最近已经证明.作者进一步证明了特征2 的带对合的除环上Hermitian 矩阵几何的基本定理, 从而得到任意带对合的除环上Hermitian 矩阵几何的基本定理.     

Harmonic maps between compact Hermitian manifolds

In this paper, we generalize the Bochner-Kodaira formulas to the case of Hermitian com- plex (possibly non-holomorphic) vector bundles over compact Hermitian (possibly non-K¨ahler) mani- folds. As applications, we get the complex analyticity of harmonic maps between compact Hermitian manifolds.     

Hessian Comparison and Spectrum Lower Bound of Almost Hermitian Manifolds

The authors obtain a complex Hessian comparison for almost Hermitian manifolds, which generalizes the Laplacian comparison for almost Hermitian manifolds by Tossati, and a sharp spectrum lower bound for compact quasi Kähler manifolds and a sharp complex Hessian comparison on nearly Kähler manifolds that generalize previous results of Aubin, Li Wang and Tam-Yu.     

Curvature vs. Almost Hermitian Structures

A Bochner-type formula for almost Hermitian manifolds is introduced. From this formula, one can find obstructions imposed by the curvature to the existence of certain almost Hermitian structures on compact manifolds.     

HERMITIAN-EINSTEIN METRICS FOR HIGGS BUNDLES OVER COMPLETE HERMITIAN MANIFOLDS

In this paper, we solve the Dirichlet problem for the Hermitian-Einstein equations on Higgs bundles over compact Hermitian manifolds. Then we prove the existence of the Hermitian-Einstein metrics on Higgs bundles over a class of complete Hermitian manifolds.     

Twistorial examples of almost Hermitian manifolds with Hermitian Ricci tensor

We construct new twistorial examples of non-Kähler almost Hermitian manifolds with Hermitian Ricci tensor by means of a natural almost Hermitian structures on the twistor space of an almost Hermitian four manifold.     

A boundary value problem for Hermitian harmonic maps and applications

We study the existence and uniqueness problems for Hermitian harmonic maps from Hermitian manifolds with boundary to Riemannian manifolds of nonpositive sectional curvature and with convex boundary. The complex analyticity of such maps and the related rigidity problems are also investigated.

     

Curvature identities on almost Hermitian manifolds and applications

We systematically derive the Bianchi identities for the canonical connection on an almost Hermitian manifold.Moreover,we also compute the curvature tensor of the Levi-Civita connection on almost Hermitian manifolds in terms of curvature and torsion of the canonical connection.As applications of the curvature identities,we obtain some results about the integrability of quasi K¨ahler manifolds and nearly K¨ahler manifolds.     

Hermitian harmonic maps from complete manifolds into convex balls

In this paper, we prove the existence and uniqueness of Hermitian harmonic maps from complete Hermitian manifolds into convex balls.     

Conformal Riemannian P-manifolds with connections whose curvature tensors are Riemannian P-tensors

The largest class of Riemannian almost product manifolds, which is closed with respect to the group of the conformal transformations of the Riemannian metric, is the class of the conformal Riemannian P-manifolds. This class is an analogue of the class of the conformal Kähler manifolds in almost Hermitian geometry. The main aim of this work is to obtain properties of manifolds of this class with connections, whose curvature tensors have similar properties as the Kähler tensors in Hermitian geometry.