Absos Ali Shaikh, Chandan Kumar Mondal, Prosenjit Mandal
Published 2020-03-11Version 1
In this paper we have investigated some aspects of gradient $\rho$-Einstein Ricci soliton in a complete Riemannian manifold. First, we have proved that the compact gradient $\rho$-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 $\rho$-Einstein soliton satisfying some integral condition, the scalar curvature vanishes.
Some results in $η$-Ricci Soliton and gradient $ρ$-Einstein soliton in a complete Riemannian manifold
Integral Liouville theorem in a complete Riemannian manifold
On conjugate points and geodesic loops in a complete Riemannian manifold
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