Quarter-symmetric metric connection in a Kenmotsu manifold

Abstract

We consider a quarter-symmetric metric connection in a Kenmotsu manifold. We investigate the curvature tensor and the Ricci tensor of a Ken- motsu manifold with respect to the quarter-symmetric metric connection. We show that the scalar curvature of an n-dimensional locally symmetric Kenmotsu manifold with respect to the quarter-symmetric metric connection is equal to n(1 - n). Furthermore, we obtain the non-existence of generalized recurrent, Φ-recurrent and pseudosymmetric Kenmotsu manifolds with respect to quarter- symmetric metric connection.