Some results on η-Ricci Soliton and gradient ρ-Einstein soliton in a complete Riemannian manifold

2018/08/14 by Shaikh, Absos Ali, Mondal, Chandan Kumar
#53C15 #53C21 #53C44 #58E20 #58J05 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.04789

Abstract

The main purpose of the paper is to prove that if a compact Riemannian manifold admits a gradient ρ-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 ρ-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 η-Ricci soliton (see Theorem 2).

Related

• Compact gradient ρ-Einstein soliton is isometric to the Euclidean sphere
• Gradient Ricci solitons carrying a closed conformal vector field
• Compact almost Ricci solitons with constant scalar curvature are gradient
• Remarks on Einstein solitons with certain types of potential vector field
• Almost η-Ricci solitons on Kenmotsu manifolds