Rigidity of Negatively Curved Locally Symmetric Spaces (Mathematics)

主要研究人员将研究如何刻画负弯曲局部对称空间的几何或动力学性质的一般问题。具体地说，她将考虑单位切丛上的时间守恒测地线流与常曲率之间的关系。她还将致力于证明：如果测地线流的度量和拓扑熵重合，并且黎曼度量是1/4-收缩的，那么流形一定有常曲率。Hamenstadt博士将教授一门关于负曲率流形几何的研究生课程；她将担任本科生荣誉数学学会Pi Mu Epsilon的顾问，并在部门研讨会上讲课。该项目进一步推动了VPW计划的目标，即：(1)为妇女提供机会，在NSF资助的工程和科学学科中发展她们的职业生涯；(2)通过提高受雇于工业、政府和学术机构的女科学家和工程师的知名度，鼓励妇女追求科学和工程事业。通过鼓励妇女参与科学，这是对国家未来科学活力的宝贵投资。

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.