Construction of Conformally Compact Einstein Manifolds

Details Construction of Conformally Compact Einstein Manifolds Construction of Conformally Compact Einstein Manifolds

2009-08-11

arxiv.org/abs/0908.1430v2

Mathematics

Differential Geometry

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

Scientific paper

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.

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