ON A SPECIAL CLASS OF HERMITIAN MANIFOLDS

J.C. MARRERO and J. ROCHA


Abstract. In this paper, we study a particular class of
hermitian manifolds which we call special $c'$-hyperbolic
hermitian manifolds with $c'\in \RR$, $c'\not= 0$. 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
$-(c')^{2}$.

Keywords: Hermitian manifolds, sasakian manifolds, kenmotsu manifolds,
hyperbolic space.

A.M.S. Classification: 53C15, 53C25, 53C55.