Speaker: 韩飞（新加坡国立大学）

Time: 14:00-15:00, Feb 26

Venue: 数学中心研讨室（至善楼602）

Online: Zoom: 811 5638 1768（Password: msrc）

Title: Generalizations of two classical theorems in Riemannian Geometry

Abstract:

The classical theorem in Riemannian geometry, the Myers’s theorem, says that a compact Riemannian manifold with positive Ricci curvature has finite fundamental group. Another classical theorem, the Bochner theorem, asserts that a compact Riemannian manifold with negative Ricci curvature has finite isometry group. In this talk, I will show how to generalize these two classical theorems to the almost nonnegative Ricci curvature and almost nonpositive Ricci curvature cases respectively. Our main tools are the Atiyah-Singer index theorem and the Bott-Taubes-Liu rigidity theorem. This represents our joint work with Xiaoyang Chen and Jian Ge.