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

2005/06/13 by Olivier Biquard, Biquard, Olivier, Marc Herzlich +3 · 1 citation
Mathematics · #32V05 #32V20 #53C20 #58J28 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:32V05 #msc:32V20 #msc:53C20 #msc:58J28

paper · pdf · doi:10.48550/arxiv.math/0506228

arxiv created 2005/06/13 · arxiv updated 2009/12/01

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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