Title：ODE Methods in Finsler Geometry
Spearker：Zhongmin Shen，Indiana University-Purdue University Indianapolis
Abstract：Finsler metrics are just Riemann metrics without quadratic restriction. There are several notions of curvatures including the Riemann curvature. These quantities interact with each other. The Hilbert metric on the unit ball in R^n is a complete reversible metric of constant flag curvature K=-1. However, Akbar-Zadeh’s Theorem asserts that any Finsler metric on a closed manifold with K=-1 must be Riemannian.
In this talk, I will briefly discuss the ODE methods used in some rigidity problems in Finsler geometry.