Concircular curvature on warped product manifolds and applications

TL;DR

This paper explores how concircular flatness and symmetry influence warped product manifolds and their components, with applications to specific space-time models in relativity.

Contribution

It investigates the effects of concircular flatness and symmetry on warped product manifolds and applies findings to generalized Robertson-Walker and static space-times.

Findings

Concircular flatness affects the structure of fiber and base manifolds.

Divergence-free concircular curvature tensor has specific properties on warped products.

Results are applicable to models in general relativity.

Abstract

This study aims mainly at investigating the effects of concircular flatness and concircular symmetry of a warped product manifold on its fibre and base manifolds. Concircularly flat and concircularly symmetric warped product manifolds are investigated. The divergence free concircular curvature tensor on warped product manifolds is considered. Finally, we apply some of these results to generalized Robertson-Walker and standard static space-times.