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 ?-Einstein manifolds. We show that a locally conformally flat
para-Kenmotsu manifold is a space of constant negative sectional curvature
-1 and we prove that if a para-Kenmotsu manifold is a space of constant
?-para-holomorphic sectional curvature H, then it is a space of constant
sectional 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 ?-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 sectional curvature -1.
Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature
