ON KENMOTSU MANIFOLDS WITH SEMI-SYMMETRIC METRIC CONNECTION

Abstract

The aim of the present paper is to study the properties of locally and globally $\phi$-concircularly symmetric Kenmotsu manifolds endowed with a semi-symmetric metric connection. First, we will prove that the locally $\phi$-symmetric and the globally $\phi$-concircularly symmetric Kenmotsu manifolds are equivalent. Next, we will study three dimensional locally $\phi$-symmetric, locally $\phi$-concircularly symmetric and locally $\phi$-concircularly recurrent Kenmotsu manifolds with respect to such connection and will obtain some geometrical results. In the end, we will construct a non-trivial example of Kenmotsu manifold admitting a semi-symmetric metric connection and validate our results.