The Sasaki-Kenmotsu manifolds

Abstract

In the present paper, we introduce a new class of structures on an even dimensional differentiable Riemannian manifold which combines, well known in literature, the Sasakian and Kenmotsu structures simultaneously. The structure will be called a Sasaki–Kenmotsu structure by us. Firstly, we discuss the normality of the Sasaki–Kenmotsu structure and give some basic properties. Secondly, we present some important results concerning with the curvatures of the Sasaki–Kenmotsu manifold. Finally, we show the existence of the Sasaki–Kenmotsu structure by giving some concrete examples.