FANO MANIFOLDS, CONTACT STRUCTURES, AND QUATERNIONIC GEOMETRY

Let Z be a compact complex (2n+1)-manifold which carries a complex contact structure, meaning a codimension-l holomorphic sub-bundle D subset of TZ which is maximally non-integrable. If Z admits a Kahler-Einstein metric of positive scalar curvature, we show that it is the Salamon twister space of a quaternion-Kahler manifold (M(4n), g). If Z also admits a second complex contact structure ($) over tilde D not equal D, then Z = CP2n+1. As an application, we give several new characterizations of the Riemannian manifold HPn = Sp(n+1)/(Sp(n) x Sp(1)).