2002/10/04 by Olivier Biquard, Biquard, Olivier
Mathematics · Physics and Astronomy · #53C26 #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C26
paper · pdf · doi:10.48550/arxiv.math/0210059
Typos corrected
openalex publication_date 2002/10/04 · arxiv created 2004/02/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).