##### Department of Mathematics,

University of California San Diego

****************************

### Math 258 - Seminar of Differential Geometry

## Xiaolong Li

#### Wichita

## Curvature operator of the second kind and proof of Nishikawa's conjecture

##### Abstract:

In 1986, Nishikawa conjectured that a closed Riemannian manifold with positive curvature operator of the second kind is diffeomorphic to a spherical space form and a closed Riemannian manifold with nonnegative curvature operator of the second kind is diffeomorphic to a Riemannian locally symmetric space. Recently, the positive case of Nishikawa's conjecture was proved by Cao-Gursky-Tran and the nonnegative case was settled by myself. In this talk, I will first talk about curvature operators of the second kind and then present a proof of Nishikawa's conjecture under weaker assumptions.

### February 3, 2022

### 11:00 AM

AP&M Room 7321

Zoom ID: 949 1413 1783

****************************