English

Construction of Conformally Compact Einstein Manifolds

Differential Geometry 2009-10-27 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.0908.1430,
  title  = {Construction of Conformally Compact Einstein Manifolds},
  author = {Dezhong Chen},
  journal= {arXiv preprint arXiv:0908.1430},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T13:34:14.295Z