On a special class of hermitian manifolds

Abstract

In this pape, we study a particular class of hermitian manifolds which we call special c’- hyperbolic hermitian manifolds with c’ Ꜫ IR, c’ ≠ 0. As main result we prove that the universal covering space of a special c’ hyperbolic hermitian manifold is the product of a c-sasakian manifold with a hyperbolic space of odd dimension and of constant sectional curvature –(c’)2.