Bounded Geodesics on Locally Symmetric Spaces

Speaker :Chengyang Wu
Time: 23 July, 2pm
Location: room 710, SIMIS

Abstract: For a general noncompact complete Riemannian manifold, it is of particular interest to know whether there exists a bounded geodesics on it or not. In 1980s, S. G. Dani proved that for a Riemannian manifold M of constant curvature and finite Riemannian volume, the set of bounded geodesics on M has the same Hausdorff dimension as the unit tangent bundle of M. In a recent paper we generalize Dani’s result to any locally symmetric space with finite volume. Moreover, for a special locally symmetric space SO_3(Z)\SL_3(R)/SL_3(Z), we can prove a winning property (stronger than full Hausdorff dimension) of the aforementioned set. This is a joint work with Lifan Guan.