Some characterizations of ρ-Einstein solitons

JOURNAL OF GEOMETRY AND PHYSICS

卷:166

Article

Shaikh, Absos Ali¹  Cunha, Antonio W.²  Mandal, Prosenjit¹ 

[1] Univ Burdwan, Dept Math, Burdwan 713104, W Bengal, India

[2] Univ Fed Piaui, Dept Matemat, BR-64049550 Teresina, Piaui, Brazil

关键词: rho-Einstein solitons;    Scalar curvature;    Harmonic function;    Traceless Ricci solitons;    Riemannian manifolds;    Parabolicity;   

DOI  :  10.1016/j.geomphys.2021.104270

来源: Elsevier

【 摘 要 】

In this article we have showed that a gradient rho-Einstein soliton with a vector field of bounded norm and satisfying some other conditions is isometric to the Euclidean sphere. Later, we have proved that a non-trivial complete gradient rho-Einstein soliton with finite weighted Dirichlet integral and certain restriction on Ricci curvature must be of constant scalar curvature and steady Ricci flat. Finally, we have proved that a non-shrinking or non-expanding gradient traceless Ricci soliton possessing some conditions must be steady. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free