Mathematical Sciences: Some Spectral and Isospectral Problems in Riemannian Geometry

数学科学：黎曼几何中的一些谱和等谱问题

• 批准号: 9006092
• 负责人: Peter Perry
• 金额: $ 4.26万
• 依托单位: University of Kentucky Research Foundation
• 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: 1990-06-15 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9006092&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Spectral; Isospectral

The principal investigator will continue his research in two areas of spectral geometry. The first involves isospectral three dimensional manifolds with curvature assumptions but no restriction on conformal class. In the second project he will develop a trace formula and Selberg zeta function for arbitrary geometrically finite discrete groups whose fundamental regions have infinite hyperbolic volume. The principal investigator will extend his theories of isospectral manifolds which are not necessarily isometric. In two dimensions, isospectral manifolds are surfaces which sound alike when struck. In higher dimensions, examples are known of hypersurfaces which sound alike but which are not isometric; that is, they do not have identical shapes.

首席研究人员将继续在光谱几何区域的两个领域进行研究。 第一个涉及具有曲率假设的同一光谱三维流形，但对保形类别没有限制。 在第二个项目中，他将为任意几何有限的离散组开发痕量公式和Selberg zeta函数，其基本区域具有无限的双曲线体积。 首席研究人员将扩展其对不一定等距的同一歧管理论。 在两个维度上，同一歧管是击中时听起来像是听起来相似的表面。 在较高的维度中，已知的示例是听起来相似但不是等距的高度曲面。也就是说，它们没有相同的形状。