FANO MANIFOLDS WITH GEOMETRIC STRUCTURES MODELED AFTER HOMOGENEOUS CONTACT MANIFOLDS

Abstract

In this paper we present a study on geometric structures modeled after homogeneous contact manifolds and show that on Fano manifolds these geometric structures are locally isomorphic to the standard geometric structures on the model spaces. This conclusion is analogous to those of [13, 7]. We expect that this work will help prove the conjecture that a compact quaternionic Kähler manifold of positive scalar curvature is a quaternionic symmetric space [21].