复流形是多复变函数和复几何的基本研究对象。复流形研究的一个核心问题是复流形的复结构、拓扑、和曲率的制约关系。比如考虑Hermitian流形上用陈联络定义的双截曲率和全纯截面曲率，一个自然的问题是研究具正(非负)、负(非正)曲率、或者曲率满足某种特殊性质的Hermitian流形的几何，凯勒流形是Hermitian流形一个重要例子。本项目研究课题：.1. 具有非负双截曲率的完备非紧凯勒流形的全纯函数。.2. 具正(非负)全纯截面曲率的紧致凯勒流形和Hermitian流形。.3. 一类给定的黎曼流形上的正交复结构的分类问题。.4. 复欧式空间中的有界拟凸域的复几何，以及具有负(非正)双截曲率的完备凯勒流形的研究。

Complex manifolds are basic objects in the study of several complex variables and complex geometry. A central topic in the study of complex manifolds is the interaction between topology, curvature, and complex structure. For example, one may consider the bisectional curvature and holomorphic sectional curvature defined by the Chern connection on Hermitian manifolds. A natural question is to study Hermitian manifolds with positive (nonnegative) or negative (nonpositive) bisectional curvature (holomorphic sectional curvature), In general Hermitian manifolds whose curvatures satisfy some special algebraic properties are objects of interest. Recall that Kähler manifolds belong to an important class of Hermitian manifolds. We will study the following topics:.1. Function theory on complete noncompact Kähler manifolds with nonnegative bisectional curvature..2. Compact Kähler manifolds and Hermitian manifolds with positive (nonnegative) holomorphic sectional curvature..3. The classification problem of the space of orthogonal complex structures on a certain class of Riemannian manifolds..4. Complex geometry of bounded pseudoconvex domains in complex Euclidean spaces, and the study of complete Kähler manifolds with negative (nonpositive) bisectional curvature.