ON A SEMI-SYMMETRIC NON-METRIC CONNECTION IN AN ALMOST KENMOTSU MANIFOLD WITH NULLITY DISTRIBUTION

Abstract

We consider a semisymmetric non-metric connection in an almost Kenmotsu manifold with its characteristic vector field $\xi$ belonging to the $(k,\mu)'$-nullity distribution. We first obtain the expressions of the curvature tensor and Ricci tensor with respect to the semisymmetric non-metric connection in an almost Kenmotsu manifold with $\xi$ belonging to the $(k,\mu)'$-nullity distribution. Then we characterize an almost Kenmotsu manifold with $\xi$ belonging to the $(k,\mu)'$-nullity distribution.