Real Submanifolds and Holomorphic Mappings in Several Complex Variables

9704835宫这个项目的目的是了解复数空间中实子流形的结构和不变量。研究了复欧氏空间中一类满足一定二阶微分关系的实流形的全实嵌入。他将研究这种嵌入的全局拓扑性质，以及实子流形的复切性与实子流形的结构相对于复欧氏空间上的全纯体积形式所产生的奇异性之间的关系。子流形是空间中曲面的高维模拟；复空间是基于复数的实空间的推广。复数空间中的实子流形很有趣，因为它们既表现出基于实数的特征，也表现出基于复数的特征。它们也作为全纯域的边界出现，这意味着它们限定了可以定义一类相当特殊的复值函数的区域。

9704835 Gong This project aims to understand structures and invariants of real submanifolds in complex spaces. The investigator is to study a class of totally real embeddings of real manifolds in the complex Euclidean space which satisfy a certain second order differential relation. He is to investigate the global topological property of such embeddings and the relationship between the complex tangency of real submanifolds and the singularity arising from the structure of real submanifolds with respect to the holomorphic volume form on the complex Euclidean space. Submanifolds are higher dimensional analogs of surfaces in space; complex spaces are generalizations of real spaces based on complex numbers. Real submanifolds in complex spaces are interesting in that they exhibit both real and complex number based characteristics. They also arise as the boundaries of domains of holomorphy, meaning that they bound regions on which a rather special class of complex-valued functions can be defined.