#### Vol. 288, No. 2, 2017

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Bach-flat $h$-almost gradient Ricci solitons

### Gabjin Yun, Jinseok Co and Seungsu Hwang

Vol. 288 (2017), No. 2, 475–488
##### Abstract

On an $n$-dimensional complete manifold $M$, consider an $h$-almost gradient Ricci soliton, which is a generalization of a gradient Ricci soliton. We prove 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. Moreover, if the dimension of $M$ is four, the metric $g$ is locally conformally flat.

##### Keywords
$h$-almost gradient Ricci soliton, Bach-flat, Einstein metric
##### Mathematical Subject Classification 2010
Primary: 53C25, 58E11