On K-contact metric manifolds satisfying an almost gradient Ricci-Bourguignon soliton

초록

The main purpose of the paper is to study an almost gradient Ricci-Bourguignon soliton (RB soliton) within the framework of K-contact manifolds and (kappa,psi)-contact manifolds. First, we prove that if complete K-contact manifold endows a gradient RB soliton, then the manifold is compact Sasakian and isometric to unit sphere S2n+1. Next, we show that if a complete contact metric satisfies an almost RB soliton with a non-zero potential vector field is collinear with the Reeb vector field xi and the Reeb vector field xi acting as an eigenvector of the Ricci operator, then it is compact Einstein Sasakian and the potential vector field is a constant multiple of the Reeb vector field xi. Lastly, we prove that if the metric of a non-Sasakian (kappa,psi)-contact manifold is an almost gradient RB soliton, then it is flat in dimension 3 and in higher dimensions it is locally isometric to E(n+1)xS(n)(4).

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