Real Submanifolds and Holomorphic Mappings in Several Complex Variables

小行星9704835 这个项目旨在理解复杂空间中真实的子流形的结构和不变量。研究复欧氏空间中真实的流形满足一定二阶微分关系的一类全真实的嵌入。他是调查的全球拓扑性质的这种嵌入和关系的复杂切线的真实的子流形和奇异性所产生的结构真实的子流形相对于全纯体积形式的复杂欧几里德空间。 子流形是空间中曲面的高维类似物;复空间是基于复数的真实的空间的推广。复空间中的真实的子流形是有趣的，因为它们表现出基于真实的和基于复数的特征。它们也作为全纯域的边界出现，这意味着它们限制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.