English

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 ρ\rho-Einstein Ricci soliton in a complete Riemannian manifold. First, we have proved that the compact gradient ρ\rho-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 ρ\rho-Einstein soliton satisfying some integral condition, the scalar curvature vanishes.

Keywords

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

R2 v1 2026-06-23T14:11:27.725Z