Compact gradient $\rho$-Einstein soliton is isometric to the Euclidean sphere
Differential Geometry
2020-03-12 v1
Abstract
In this paper we have investigated some aspects of gradient -Einstein Ricci soliton in a complete Riemannian manifold. First, we have proved that the compact gradient -Einstein soliton is isometric to the Euclidean sphere by showing that the scalar curvature becomes constant. Second, we have showed that in a non-compact gradient -Einstein soliton satisfying some integral condition, the scalar curvature vanishes.
Cite
@article{arxiv.2003.05234,
title = {Compact gradient $\rho$-Einstein soliton is isometric to the Euclidean sphere},
author = {Absos Ali Shaikh and Chandan Kumar Mondal and Prosenjit Mandal},
journal= {arXiv preprint arXiv:2003.05234},
year = {2020}
}
Comments
6 pages