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 × f M n . Furthermore, we characterize rotational hypersurface into R × f R n has a gradient Einstein-type structure.