Characterization of sequential warped product gradient Ricci-Bourguignon soliton


Sampa Pahan, Souvik Dutta




In this paper, we study 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 M 1 and M 3 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.