On the H-almost ricci soliton

J. N. Gomes; Qiaoling Wang; Changyu Xia

On the H-almost ricci soliton

Differential Geometry 2015-05-05 v2

Authors: J. N. Gomes , Qiaoling Wang , Changyu Xia

Abstract

We introduce the concept {\it $h$ -almost Ricci soliton} which extends naturally the {\it almost Ricci soliton} by Pigola-Rigoli-Rimoldi-Setti and show that a compact nontrivial $h$ -almost Ricci soliton of dimension no less than three with $h$ having defined signal and constant scalar curvature is isometric to a standard sphere with the potential function well determined. We also consider the {\it $h$ -Ricci soliton} which is a particular case of the $h$ -almost Ricci soliton and a generalization of the {\it Ricci soliton} and give characterizations for a special class of gradient $h$ -Ricci solitons.

Keywords

h-almost ricci soliton ricci soliton compact manifold constant scalar curvature standard sphere gradient solitons isometry

Cite

@article{arxiv.1411.6416,
  title  = {On the H-almost ricci soliton},
  author = {J. N. Gomes and Qiaoling Wang and Changyu Xia},
  journal= {arXiv preprint arXiv:1411.6416},
  year   = {2015}
}

Comments

9 pages. This is a revised version of the previous paper "h-almost Ricci soliton"

On the H-almost ricci soliton

Abstract

Keywords

Cite

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