Generalized Kenmotsu Manifolds

Aysel Turgut Vanli, Ramazan Sari

Abstract


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 \(\varphi\)-sectional curvature of any semi-symmetric and projective semi-symmetric \((2n+s)\)-dimensional generalized Kenmotsu manifold is \(-s\).

Keywords


Kenmotsu manifolds, metric f-manifolds, generalized Kenmotsu manifolds, semi-symmetric, Ricci semi-symmetric, projective semi-symmetric.

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v7i4.471

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