  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 $-1$.
