The W-2-curvature tensor on warped product manifolds and applications

Abstract

The purpose of this paper is to study the W-2-curvature tensor on (singly) warped product manifolds as well as on generalized Robertson-Walker and standard static space-times. Some different expressions of the W-2-curvature tensor on a warped product manifold in terms of its relation with W-2-curvature tensor on the base and fiber manifolds are obtained. Furthermore, we investigate W-2-curvature flat warped product manifolds. Many interesting results describing the geometry of the base and fiber manifolds of a W-2-curvature flat warped product manifold are derived. Finally, we study the W-2-curvature tensor on generalized Robertson-Walker and standard static space-times; we explore the geometry of the fiber of these warped product space-time models that are W-2-curvature flat.