Mathematical Sciences: Complex Manifold Theory and Kaehler Geometry

数学科学：复流形理论和凯勒几何

• 批准号: 9500999
• 负责人: Yum-Tong Siu
• 金额: $ 27.75万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 2002-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500999&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Complex; Manifold; Theory

DMS-9500999 Siu Siu will investigate several related problems in complex manifold theory and Kaehler geometry. These include hyperbolicity problems, effective freeness and very ampleness, general Bochner type formula and geometric superrigidity, and global nondeformability of compact hermitian symmetric manifolds. Several complex variables arose at the beginning of the century as a natural outgrowth of studies of functions of one complex variable. It became clear early on that the theory differed widely from it predecessor. The underlying geometry was far more difficult to grasp and the function theory had far more affinity with partial differential operators of first order. It thus grew as a hybrid subject combining deep characteristics of differential geometry and differential equations. Many of the fundamental structures were defined in the last three decades. Current studies still concentrate on understanding these basic mathematical forms.

DMS-9500999 Siu Siu将研究复流形理论和凯勒几何中的几个相关问题。这些问题包括双曲性问题、有效自由性和非常广度问题、一般Bochner型公式和几何超刚性以及紧致厄米特对称流形的整体不可变性。本世纪初出现了几个复变量，这是一个复变量函数研究的自然结果。很早就很明显，这一理论与其前身有很大不同。基本的几何学要难得多，而函数论与一阶偏微算符的亲和力要强得多。因此，它成长为一门混合学科，结合了微分几何和微分方程式的深刻特征。许多基本结构都是在过去30年里定义的。目前的研究仍然集中在理解这些基本的数学形式上。