Investigations of warped product manifolds through the concircular curvature tensor with relativistic applications

Abstract

This article focuses on characterizing warped product manifolds through the flatness and the symmetry of the concircular curvature tensor. It is proved that the factor manifolds of a concircularly-flat warped product manifold have constant sectional curvatures as well as they are concircularly-flat. It is shown that in a concircularly-symmetric warped product manifold, the fiber manifold has constant sectional curvature and it is concircularly-flat, while the base manifold is locally-symmetric and concircularly-symmetric. It is demonstrated that a concircularly-flat (symmetric) GRW space-time is perfect fluid and static. Finally, it is established that in a concircularly-flat (symmetric) F-associated standard static space-time, the base manifold has constant sectional curvature and it is concircularly-flat, while the fiber manifold is locally-symmetric and concircularly-symmetric.