Compact almost Ricci solitons with constant scalar curvature are gradient

Abdênago Barros; Rondinelle Batista; Ernani Ribeiro

Compact almost Ricci solitons with constant scalar curvature are gradient

Differential Geometry 2013-09-27 v3

Authors: Abdênago Barros , Rondinelle Batista , Ernani Ribeiro

Abstract

The aim of this note is to prove that any compact non-trivial almost Ricci soliton $\big(M^n,\,g,\,X,\,\lambda\big)$ with constant scalar curvature is isometric to a Euclidean sphere $\Bbb{S}^{n}$ . As a consequence we obtain that every compact non-trivial almost Ricci soliton with constant scalar curvature is gradient. Moreover, the vector field $X$ decomposes as the sum of a Killing vector field $Y$ and the gradient of a suitable function.

Keywords

almost Ricci soliton constant scalar curvature compact manifold gradient Killing vector field Euclidean sphere

Cite

@article{arxiv.1209.2720,
  title  = {Compact almost Ricci solitons with constant scalar curvature are gradient},
  author = {Abdênago Barros and Rondinelle Batista and Ernani Ribeiro},
  journal= {arXiv preprint arXiv:1209.2720},
  year   = {2013}
}

Comments

To appear in Monatshefte fur Mathematik

Compact almost Ricci solitons with constant scalar curvature are gradient

Abstract

Keywords

Cite

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