Mathematical Sciences: Manifolds With Non-Negative Curvature

数学科学：非负曲率流形

• 批准号: 9003524
• 负责人: David Yang
• 金额: $ 4.43万
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-07-15 至 1993-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9003524&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Manifolds; Non; Negative

The principal investigator will conduct research into Riemannian manifolds with positive Ricci curvature and harmonic maps between spheres. He will investigate as to whether products of two closed 1-connected manifolds must have positive Ricci curvature when each has such curvature. And he will investigate the problem of whether closed 1-connected 5-manifolds carry metrics with positive Ricci curvature. The study of differential geometry has focused on problems concerning curvature for over a century. Today there are several competing notions of curvature including sectional, Gauss, and Ricci. Recently, in collaboration, the principal investigator constructed a complete Riemannian manifold with positive Ricci curvature which did not have non-negative sectional curvature. In this project he will study related questions for hypersurfaces of dimension four and five.

首席研究者将对带有正面曲率和谐波图的Riemannian歧管进行研究。 他将调查两个封闭的1个封闭歧管的产物是否在每个曲率上时都必须具有正RICCI曲率。 他将研究是否关闭1个相互连接的5个manifolds携带呈正曲率的指标。 差异几何形状的研究集中在一个多世纪以来的曲率问题上。 如今，有几个相互竞争的曲率概念，包括分段，高斯和里奇。 最近，在合作中，主要研究人员建造了一个完整的Riemannian歧管，其正曲率为正曲率，该曲率没有非负分段曲率。 在这个项目中，他将研究第四和五个维度的超曲面相关问题。