On $phi$-recurrent Kenmotsu manifolds

Abstract

The object of this paper is to study $phi$-recurrent Kenmotsu manifolds. Also three-dimensional locally $phi$- recurrent Kenmotsu manifolds have been considered. Among others it is proved that a locally $phi$-recurrent Kenmotsu spacetime is the Robertson-Walker spacetime. Finally we give a concrete example of a threedimensional Kenmotsu manifold.