Rigidity of Negatively Curved Locally Symmetric Spaces (Mathematics)

负曲局部对称空间的刚性（数学）

• 批准号: 8902678
• 负责人: Ursula Hamenstadt
• 金额: --
• 依托单位: University of Pennsylvania
• 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: 1990-07-01 至 1991-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902678&HistoricalAwards=false
• 关键词: Rigidity; Negatively; Curved; Locally; Symmetric

The principal investigator will study the general problem of how geometric or dynamic properties characterize negatively curved locally symmetric spaces. Specifically, she will consider the relationship between time-preserving geodesic flows on the unit tangent bundle, and constant curvature. She will also work toward proving that if the metric and topological entropy of a geodesic flow coincide, and the Riemannian metric is 1/4-pinched, then the manifold must have constant curvature. Dr. Hamenstadt will teach a graduate course in the geometry of manifolds of negative curvature; she will serve as an advisor for the undergraduate honors mathematics society, Pi Mu Epsilon, and lecture in departmental seminars. This project furthers VPW program objectives which are (1) to provide opportunities for women to advance their careers in engineering and in the disciplines of science supported by NSF and (2) to encourage women to pursue careers in science and engineering by providing greater visibility for women scientists and engineers employed in industry, government, and academic institutions. By encouraging the participation of women in science, it is a valuable investment in the Nation's future scientific vitality.

首席研究员将研究如何 几何或动力学性质表征负弯曲局部 对称空间。 具体来说，她会考虑 单位切丛上的保时测地线流之间，以及 常曲率 她还将努力证明，如果 度量和拓扑熵的测地线流一致，和 黎曼度量是1/4-箍缩的，则流形必有常数 曲率 Hamenstadt博士将教授一门研究生课程， 负曲率的流形;她将担任顾问的 本科生荣誉数学学会，皮穆埃珀里，和讲座 在部门研讨会上 该项目进一步促进了VPW计划的目标，即（1）提供 为妇女提供在工程和技术领域发展职业生涯的机会 由NSF支持的科学学科和（2）鼓励 妇女追求科学和工程事业， * 提高妇女科学家和工程师的知名度， 行业、政府和学术机构。 通过鼓励 妇女参与科学，这是一项宝贵的投资， 国家未来的科学活力。