ON HYPERBOLIC KENMOTSU MANIFOLDS WITH THE GENERALIZED SYMMETRIC METRIC CONNECTION

In this paper, we define Hyperbolic Kenmotsu manifolds and the generalized symmetric metric connection on this manifold. Further we discuss curvature tensor and Ricci curvature tensor with respect to the generalized symmetric metric connection. We also study Ricci semi-symmetric 3-dim Hyperbolic Kenmotsu manifold with the generalized symmetric metric connection and Projectively flat manifold with respect to the generalized symmetric metric connection.