Mathematical Sciences: RUI: Geometry of Submanifolds

数学科学：RUI：子流形几何

• 批准号: 9101961
• 负责人: Thomas Cecil
• 金额: --
• 依托单位: College of the Holy Cross
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9101961&HistoricalAwards=false
• 关键词: Mathematical; Sciences; RUI; Geometry; Submanifolds

The principal investigator will continue his study of submanifolds of the simply connected constant curvature manifolds using the techniques of Lie sphere geometry. In particular he will attempt to give a classification of the taut and Dupin submanifolds. The investigator will also continue to involve undergraduate students in his research thus providing them with a solid background for graduate study. The simply connected constant curvature manifolds are Euclidean space, the sphere, and hyperbolic space. These manifolds are very special and serve as test cases for many questions in differential geometry. The principal investigator will attempt to classify all submanifolds or surfaces in these manifolds which are taut or rigid.

主要研究者将继续利用李球几何的技巧研究单连通常曲率流形的子流形。特别是，他将尝试给出张子流形和杜平子流形的分类。调查员还将继续让本科生参与他的研究，从而为他们的研究生学习提供坚实的背景。单连通的常曲率流形是欧氏空间、球面和双曲空间。这些流形非常特殊，可以作为微分几何中许多问题的测试用例。首席研究员将尝试对这些流形中的所有紧致或刚性的子流形或曲面进行分类。