A Study of Generalized Projective P−Curvature Tensor on Warped Product Manifolds

The main aim of this study is to investigate the effects of the P−curvature flatness, P−divergence-free characteristic, and P−symmetry of a warped product manifold on its base and fiber (factor) manifolds. It is proved that the base and the fiber manifolds of the P−curvature flat warped manifold are Einstein manifold. Besides that, the forms of the P−curvature tensor on the base and the fiber manifolds are obtained. The warped product manifold with P−divergence-free characteristic is investigated, and amongst many results, it is proved that the factor manifolds are of constant scalar curvature. Finally, P−symmetric warped product manifold is considered.