Some results in $\eta$-Ricci soliton and gradient $\rho$-Einstein soliton in a complete Riemannian manifold
Commun. Korean Math. Soc. 2019 Vol. 34, No. 4, 1279-1287
https://doi.org/10.4134/CKMS.c180347
Published online October 31, 2019
Chandan Kumar Mondal, Absos Ali Shaikh
The University of Burdwan; The University of Burdwan
Abstract : The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient $\rho$-Einstein soliton such that the gradient Einstein potential is a non-trivial conformal vector field, then the manifold is isometric to the Euclidean sphere. We have showed that a Riemannian manifold satisfying gradient $\rho$-Einstein soliton with convex Einstein potential possesses non-negative scalar curvature. We have also deduced a sufficient condition for a Riemannian manifold to be compact which satisfies almost $\eta$-Ricci soliton.
Keywords : gradient $\rho$-Einstein soliton, almost $\eta$-Ricci soliton, Hodge-de Rham potential, Einstein potential, convex function, harmonic function, conformal vector field
MSC numbers : Primary 53C15, 53C21, 53C44, 58E20, 58J05
Downloads: Full-text PDF   Full-text HTML

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd