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Autodual Einstein Versus Kähler–Einstein

Name: Autodual Einstein Versus Kähler–Einstein
Creator: Olivier Biquard
Keywords: Mathematics - Differential Geometry, Local differential geometry of Hermitian and Kählerian structures, Kähler-Einstein manifolds, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), CR structures, Global differential geometry of Hermitian and Kählerian manifolds, Analysis on CR manifolds, 01 natural sciences, 53C26, Special Riemannian manifolds (Einstein, Sasakian, etc.)

Autodual Einstein versus Kähler-Einstein

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2005Embargo end date: 01 Jan 2002Publisher:Springer Science and Business Media LLCJournal:GAFA Geometric And Functional Analysis, volume 15, pages 598-633 (issn: 1016-443X, eissn: 1420-8970,

Authors: Olivier Biquard;

doi: 10.1007/s00039-005-0520-0 , 10.48550/arxiv.math/0210059

arXiv: http://arxiv.org/abs/math/0210059

Autodual Einstein Versus Kähler–Einstein

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Abstract

Any strictly pseudoconvex domain in C2 carries a complete Kahler-Einstein metric, the Cheng-Yau metric, with ``conformal infinity'' the CR structure of the boundary. It is well known that not all CR structures on the 3-sphere arise in this way. In this paper, we study CR structures on the 3-sphere satisfying a different filling condition: boundaries at infinity of (complete) selfdual Einstein metrics. We prove that (modulo contactomorphisms) they form an infinite dimensional manifold, transverse to the space of CR structures which are boundaries of complex domains (and therefore of Kahler-Einstein metrics).

Typos corrected

Related Organizations

Centre national de la recherche scientifique
France

Keywords

Mathematics - Differential Geometry, Local differential geometry of Hermitian and Kählerian structures, Kähler-Einstein manifolds, Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills), CR structures, Global differential geometry of Hermitian and Kählerian manifolds, Analysis on CR manifolds, 53C26, Special Riemannian manifolds (Einstein, Sasakian, etc.), Differential Geometry (math.DG), boundaries at infinity, FOS: Mathematics

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