Real Submanifolds and Holomorphic Mappings in Several Complex Variables

多个复变量中的实子流形和全纯映射

• 批准号: 9704835
• 负责人: Xianghong Gong
• 金额: $ 7.01万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-15 至 1999-10-27
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704835&HistoricalAwards=false
• 关键词: Real; Submanifolds; Holomorphic; Mappings; Several

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.

这个项目旨在理解复空间中实子流形的结构和不变量。研究复欧几里德空间中满足一定二阶微分关系的实数流形的一类全实数嵌入。他将研究这种嵌入的整体拓扑性质，以及实子流形的复切与实子流形结构在复欧几里德空间上的全纯体积形式所产生的奇点之间的关系。子流形是空间中曲面的高维类似物；复空间是基于复数的实空间的推广。复空间中的实子流形很有趣，因为它们同时表现出基于实数和复数的特征。它们也作为全纯域的边界出现，这意味着它们所限定的区域上可以定义一类相当特殊的复值函数。