##### Department of Mathematics,

University of California San Diego

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### Math 258: Seminar in Differential Geometry

## Xiaolong Li

#### Wichita

## The Curvature Operator of the Second Kind

##### Abstract:

I will first give an introduction to the notion of the curvature operator of the second kind and review some known results, including the proof of Nishikawa's conjecture stating that a closed Riemannian manifold with positive (resp. nonnegative) curvature operator of the second is diffeomorphic to a spherical space form (resp. a Riemannian locally symmetric space). Then I will talk about my recent works on the curvature operator of the second kind on Kahler manifolds and product manifolds. Along the way, I will mention some interesting questions and conjectures.

Host: Lei Ni

### October 13, 2022

### 11:00 AM

Zoom ID: 953 0943 3365

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