H-CONTACT UNIT TANGENT SPHERE BUNDLES OF EINSTEIN MANIFOLDS

Abstract

We study the geometric properties of a base manifold whose unit tangent sphere bundle equipped with the standard contact metric structure is H-contact. We shall prove that a necessary and sufficient condition for the unit tangent sphere bundle of an Einstein manifold to be H-contact is that the base manifold is 2-stein. As its applications, we give an explicit classification of such base manifolds in the special cases of irreducible symmetric spaces or of Kahler-Einstein manifolds with non-negative sectional curvature. Further, we provide examples illustrating the non-homogeneous situations in dimension four.