Bach-flat $h$-almost gradient Ricci solitons

Gabjin Yun, Jinseok Co and Seungsu Hwang

Vol. 288 (2017), No. 2, 475–488

DOI: 10.2140/pjm.2017.288.475

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

Milestones

Received: 14 April 2016

Revised: 29 September 2016

Accepted: 30 October 2016

Published: 28 April 2017