Rigidity of Negatively Curved Locally Symmetric Spaces (Mathematics)

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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.