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

Olivier Biquard·Marc Herzlich·Michel Rumin
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Abstract

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.

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Olivier Biquard, Marc Herzlich, Michel Rumin. 2005-06-13. Diabatic Limit, Eta Invariants and Cauchy-Riemann Manifolds of Dimension 3. https://arxiv.org/abs/math/0506228

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