ON 3-DIMENSIONAL $\alpha$-PARA KENMOTSU MANIFOLDS

Abstract

The aim of the present paper is to study 3-dimensional alpha-para Kenmotsu manifolds. First we consider 3-dimensional Ricci semisymmetric $\alpha$-para Kenmotsu manifolds and obtain some equivalent conditions. Next we study cyclic parallel Ricci tensor in 3-dimensional $\alpha$-para Kenmotsu manifolds. Moreover, we investigate $\eta$-parallel Ricci tensor in 3-dimensional $\alpha$-para Kenmotsu manifolds. Continuing our study, we consider locally $\phi$-symmetric 3-dimensional alpha-para Kenmotsu manifolds. Next, we study gradient Ricci solitons in 3-dimensional $\alpha$-para Kenmotsu manifolds. Finally, we give an example of a 3-dimensional $\alpha$-para Kenmotsu manifold which veries some results.