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

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Cited by in corpus (4)

• On the nonexistence of quasi-Einstein metrics
• On conformally covariant powers of the Laplacian
• Einstein Metrics from Symmetry and Bundle Constructions: A Sequel
• Examples of Einstein manifolds in odd dimensions