Vol. 288, No. 2, 2017

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ISSN: 0030-8730
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 dhdu > 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
Authors
Gabjin Yun
Department of Mathematics
Myong Ji University
San 38-2 Namdong
Yongin, Gyeonggi 449-728
South Korea
Jinseok Co
Department of Mathematics
Chung-Ang University
84 Heukseok-ro, Dongjak-gu
Seoul 06969
South Korea
Seungsu Hwang
Department of Mathematics
Chung-Ang University
84 Heuksuk-ro, Dongjak-gu
Seoul 06969
South Korea