Characterization of sequential warped product gradient Ricci-Bourguignon soliton

Abstract

In this paper, westudy characterization of sequential warped product gradient Ricci-Bourguignon soliton. We derive applications of some vector fields like torse-forming vector field, torqued vector field, conformal vector field on Ricci-Bourguignon soliton. We show that for torse-forming vector field, a Ricci- Bourguignon soliton becomes an almost quasi-Einstein manifold. Next, we obtain the inheritance properties of the Einstein-like sequential warped product gradient Ricci-Bourguignon almost soliton of class type P,A,B. We prove that, when the manifold is complete, the potential function depends only on M1 and M3 must be an Einstein manifold. We also present for a gradient Ricci-Bourguignon soliton sequential warped product, the warping functions are constants under some certain conditions.