A new characterization of Kenmotsu manifolds with respect to Q tensor

Abstract

This paper introduces a new characterization of Kenmotsu manifolds and analyzes curvature conditions of Kenmotsu manifolds admitting the Q tensor whose trace is the well-known Z tensor. New types of Kenmotsu manifold are defined which are named ϕ−Q symmetric Kenmotsu manifold and ϕ−Q recurrent Kenmotsu manifold. Various properties of such a 2m+1-dimensional Kenmotsu manifold are studied. A theorem is given which states that a three-dimensional locally ϕ−Q recurrent and locally ϕ−Q symmetric Kenmotsu manifold admitting Q tensor is a manifold of constant curvature. Some examples of locally ϕ−Q symmetric Kenmotsu manifolds and Kenmotsu manifolds admitting Q tensor are provided.