Geometric structures of sequential warped products and their relations with the gradient Ricci-Yamabe solitons

Abstract

In this paper, we investigate the geometric properties of sequential warped product manifolds which is the most general concept of the warped product manifolds. We then establish some necessary and sufficient conditions for sequential warped product manifolds admitting a gradient Ricci-Yamabe soliton. We focus particularly on the triviality of the sequential warped product manifold admitting the gradient Ricci-Yamabe soliton. For the physical applications, we investigate the behavior of these solitons in sequential generalized Robertson-Walker spacetimes and sequential standard static spacetimes.