Some characterizations of Kenmotsu manifolds admitting a quarter-symmetric metric connection

Abstract

In this paper, we study certain curvature properties of Kenmotsu manifolds with respect to the quarter-symmetric metric connection. First, we investigate Weyl projective symmetric Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Next, we study Kenmotsu manifolds satisfying the curvature condition e P̃.S = 0, where P̃ and S are the projective curvature tensor and Ricci tensor respectively with respect to the quarter symmetric metric connection. Further, we discuss pseudoprojectively at and Φ-projectively semi-symmetric Kenmotsu manifolds with respect to the quarter-symmetric metric connection. Finally, we give an example of a 5-dimensional Kenmotsu manifold admitting a quarter-symmetric metric connection for illustration.