##### Department of Mathematics,

University of California San Diego

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### Math 258 - Differential Geometry

## Seungsu Hwang

#### Chung-Ang University

## Bach-flat h-almost gradient Ricci solions

##### Abstract:

On an n-dimensional complete manifold M, consider an h-almost gradient Ricci soliton, which is a generalization of gradient Ricci solitons and $(\lambda , n + m)$-Einstein manifolds. In this talk, we show that if the manifold is Bach-flat and $dh/du > 0$, then the manifold M is either Einstein or rigid. In particular, such a manifold has harmonic Weyl curvature. When the dimension of M is four, the metric is locally conformally flat.

Host: Lei Ni

### April 11, 2018

### 2:00 PM

### AP&M 5829

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