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 . investigate conditions to be totally umbilical, or geodesic I × f M n Furthermore, rotational hypersurface R has structure.

Abstract In this paper, we study locally projectively flat Finsler metrics of constant flag curvature. We find equations that characterize these by warped product. Using the obtained equations, manufacture new product vanishing These contain metric introduced Berwald and spherically symmetric given Mo-Zhu.