January 11, 2010, 2:10 pm

Bahen 6183

Abstract:Conformally compact Einstein (CCE) manifolds are complete noncompact Einstein manifolds which is conformal to a compact Riemannian manifold-with-boundary. In this work, we construct some CCE metrics on 1. certain ball bundles over product of Kahler-Einstein manifolds, and 2. certain solid-torus bundles over Kahler-Einstein Fano manifold. Our strategy is to reduce the Einstein equation to a system of ODEs, and then solve the resulting system explicitly. As a by-product, we obtain some Riemannian manifolds with vanishing Q-curvature.