Static Perfect Fluid Space-Time on Almost Kenmotsu Manifolds

Abstract

In this work, we intend to investigate the characteristics of static perfect fluid space-time metrics on almost Kenmotsu manifolds. At first we prove that if a Kenmotsu manifold M is the spatial factor of static perfect fluid space-time then it is eta-Einstein. Moreover, if the Reeb vector field xi leaves the scalar curvature invariant, then M is Einstein. Next we consider static perfect fluid space-time on almost Kenmotsu (kappa, mu)'-manifolds and give some characteristics under certain conditions.