The space of Cauchy-Riemann structures on 3-D compact contact manifolds

2010/07/13 by John Bland, Bland, John, Tom Duchamp +1
Mathematics · #32G05(secondary) #58D05 (primary) #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #math.DG #msc:58D05

paper · pdf · doi:10.48550/arxiv.1007.2037

32 pages

arxiv created 2010/07/13 · openalex publication_date 2010/07/13 · arxiv updated 2010/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the action of the group of contact diffeomorphisms on CR deformations of compact three-dimensional CR manifolds. Using anisotropic function spaces and an anisotropic structure on the space of contact diffeomorphisms, we establish the existence of local transverse slices to the action of the contact diffeomorphism group in the neighbourhood of a fixed embeddable strongly pseudoconvex CR structure.

Related

• The Group of Contact Diffeomorphisms for Compact Contact Manifolds
• Cauchy-Riemann geometry and contact topology in three dimensions
• On transitive contact and CR algebras
• Automorphism groups of normal CR 3-manifolds
• Associated Families of Immersions of Three Dimensional CR Manifolds in Euclidean Spaces