Abstract
We consider a general notion of an almost Ricci soliton and establish some curvature properties for the case in which the potential vector field of the soliton is a generalized geodesic or a 2-Killing vector field. In this vein, we characterize trivial generalized Ricci solitons.
Highlights
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The aim of this paper is to provide some sufficient conditions for a generalized Ricci soliton on a Riemannian manifold to be trivial
We studied generalized Ricci solitons ( g, ξ, α, β) on an n-dimensional compact smooth manifold M for n > 2 by restricting the as-generalized geodesic vector field
Summary
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia; Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia These authors contributed equally to this work.
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