On α-Kenmotsu manifolds satisfying certain conditions

Abstract

The object of this paper is to study α-Kenmotsu manifolds which can be derived from almost contact Riemannian manifolds satisfying some certain conditions. We first examine the generalized recurrent α-Kenmotsu manifolds, and next we give some relations about Ricci semi-symmetric and D-conformal curvature tensors. We show that Ricci semi-symmetric α-Kenmotsu manifolds are also Einstein manifolds. Furthermore, we prove that the scalar curvature of α-Kenmotsu manifolds with η-parallel Ricci tensors is constant. We conclude the paper with an example on α-Kenmotsu manifolds. © Balkan Society of Geometers, Geometry Balkan Press 2010.