Diabatic Limit, Eta Invariants and Cauchy-Riemann Manifolds of Dimension 3

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We relate a recently introduced non-local geometric invariant of compact strictly pseudoconvex Cauchy-Riemann (CR) manifolds of dimension 3 to various eta-invariants in CR geometry: on the one hand a renormalized eta-invariant appearing when considering a sequence of metrics converging to the CR structure by expanding the size of the Reeb field; on the other hand the eta-invariant of the middle degree operator of the contact complex. We then provide explicit computations for a class of examples: transverse circle invariant CR structures on Seifert manifolds. Applications are given to the problem of filling a CR manifold by a complex hyperbolic manifold, and more generally by a Kahler-Einstein or an Einstein metric.

Keywords

Differential Geometry, 32V05; 32V20; 53C20; 58J28

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/75466

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0506228
 http://arxiv.org/abs/math/0506228

Collections

arXiv