Gradient Einstein-Type Structures immersed into a Riemannian Warped Product

Abstract

In this paper, we study gradient Einstein-type structure immersed into a Riemannian warped product manifold. We obtain some triviality results for the potential function and smooth map $u$. We investigate conditions for a gradient Einstein-type structure to be minimal, totally umbilical, or totally geodesic immersed into a warped product $I{\times }_f{M}^n$. Furthermore, we characterize rotational hypersurface into $\mathbb{R}{\times }_f{\mathbb{R}}^n$ has a gradient Einstein-type structure.

arXiv admin note: text overlap with arXiv:2010.03995