Index and stability of closed semi-Riemannian geodesics

报告题目:Index and stability of closed semi-Riemannian geodesics

报告人:Alessandro Portaluri 教授 (意大利都灵大学)

报告时间:2018.3.15 星期四 15:30-16:30

报告地点:知新楼B924报告厅

摘要:A celebrated result due to Poincaré asserts that a closed minimizing geodesic on a orientable surface is linearly unstable when considered as orbit of the co-geodesic flow.

In this talk, starting from this classical theorem, we discuss some recently new results on the instability and hyperbolicity of closed (maybe not minimizing) geodesics of any causal character on higher dimensional (even not orientable) semi-Riemannian manifolds. Dropping the non-positivity assumption of the metric tensor is a quite challenging task since the Morse index is truly infinite.

This is a joint work with Xijun Hu and Ran Yang.