- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 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.c180347Published 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