Generalized Kenmotsu Manifolds - Vanli, Aysel Turgut; Sari, Ramazan (Communications in Mathematics and Applications, 2016)
In 1972, K. Kenmotsu studied a class of almost contact Riemannian manifolds which later are called a Kenmotsu manifold. In this paper, we study Kenmotsu manifolds with \((2n+s)\)-dimensional $s$-contact metric manifold that we call generalized Kenmotsu manifolds.\ Necessary and sufficient condition is given for a \(s\)-contact metric manifold to be a generalized Kenmotsu manifold. We show that a generalized Kenmotsu manifold is a locally warped product space. In addition, we study some curvature properties of generalized Kenmotsu manifolds. Moreover, we obtain that the \(φ\)-sectional curvature of any semi-symmetric and projective semi-symmetric \((2n+s)\)-dimensional generalized Kenmotsu manifold is \(-s\).