The Bochner-flat cone of a CR manifold

Abstract

We construct a Kahler structure (which we call a generalised Kahler cone) on an open subset of the cone of a strongly pseudo-convex CR manifold endowed with a 1-parameter family of compatible Sasaki structures. We determine those generalised Kahler cones which are Bochner-flat and we study their local geometry. We prove that any Bochner-flat Kahler manifold of complex dimension bigger than two is locally isomorphic to a generalised Kahler cone.