Mathematical Sciences: Special Submanifolds

数学科学：特殊子流形

• 批准号: 9403851
• 负责人: Gary Jensen
• 金额: $ 3.6万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9403851&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Special; Submanifolds

9403851 Jensen This award supports mathematical research on problems in differential geometry. The work focuses on Dupin hypersurfaces and deformable surfaces in Lie Sphere geometry. Efforts will be made to determine whether or not there exist minimal surfaces with constant negative Gaussian curvature in the complex projective plane. The problems involve special submanifolds of great interest; their solutions involve a combination of techniques arising in the study of systems of partial differential equations combined with geometric structures. Applications of the work may be expected in mathematical physics as well as geometry. Differential geometry is a branch of mathematics which combines methods of analysis with geometric motivation. The problems often derive from those of the physical world such as would be found in studies of relativity, turbulence, dynamical systems and chaos. ***

小行星9403851 该奖项支持微分几何问题的数学研究。 主要研究李球几何中的Dupin超曲面和可变形曲面。 研究复射影平面上是否存在具有常负高斯曲率的极小曲面。 这些问题涉及特殊的子流形极大的兴趣;他们的解决方案涉及的技术相结合的研究系统的偏微分方程结合几何结构。 应用的工作可能会在数学物理以及几何。 微分几何是数学的一个分支，它把分析方法和几何学的动机结合起来。 这些问题通常来自于物理世界的问题，比如在相对论、湍流、动力系统和混沌的研究中会发现的问题。 ***