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 totally umbilical, or totally geodesic immersed into a warped product I×fMn. Furthermore, we study rotational hypersurface into R×fRn has a gradient Einstein-type structure.
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