On para-Kenmotsu manifolds

Simeon Zamkovoy


In this paper we study para-Kenmotsu manifolds.
We characterize this manifolds by tensor equations and study their properties. We are devoted to a study of $\eta-$Einstein manifolds.
We show that a conformally flat para-Kenmotsu manifold is a space of constant negative curvature $-1$
and we prove that if a para-Kenmotsu manifold is a space of constant $\varphi-$para-holomorphic sectional curvature $H$,
then it is a space of constant curvature and $H=-1$. Finally the object of the present paper is to study a 3-dimensional para-Kenmotsu manifold, satisfying certain curvature conditions.
Among other, it is proved that any 3-dimensional para-Kenmotsu manifold with $\eta-$parallel Ricci tensor is of constant scalar curvature and
any 3-dimensional para-Kenmotsu manifold satisfying cyclic Ricci tensor is a manifold of constant negative curvature $-1$.


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