The W2-curvature tensor on warped product manifolds and applications
International Journal of Geometric Methods in Modern Physics
World Scientific Publishing
1650099-1 - 1650099-14
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The purpose of this paper is to study the W2-curvature tensor on (singly) warped product manifolds as well as on generalized Robertson-Walker and standard static space-times. Some different expressions of the W2-curvature tensor on a warped product manifold in terms of its relation with W2-curvature tensor on the base and fiber manifolds are obtained. Furthermore, we investigate W2-curvature flat warped product manifolds. Many interesting results describing the geometry of the base and fiber manifolds of a W2-curvature flat warped product manifold are derived. Finally, we study the W2-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 W2-curvature flat. © 2016 World Scientific Publishing Company.
KeywordsGeneralized Robertson-Walker space-time
Standard static space-time