Construction of Conformally Compact Einstein Manifolds

Abstract

We produce some explicit examples of conformally compact Einstein manifolds, whose conformal compactifications are foliated by Riemannian products of a closed Einstein manifold with the total space of a principal circle bundle over products of Kahler-Einstein manifolds. We compute the associated conformal invariants, i.e., the renormalized volume in even dimensions and the conformal anomaly in odd dimensions. As a by-product, we obtain some Riemannian products with vanishing Q-curvature.

40 pages, no figures, add Remark 1.13 and Note added in proof

References in corpus (2)

• Riemannian products which are conformally equivalent to Einstein metrics
• On Ricci solitons of cohomogeneity one