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

TL;DR

This paper investigates the structure of CR deformations on 3D compact contact manifolds, establishing local slices to the contact diffeomorphism group's action using anisotropic function spaces.

Contribution

It introduces a novel anisotropic framework to analyze the action of contact diffeomorphisms on CR structures, proving the existence of local transverse slices.

Findings

Existence of local transverse slices near embeddable CR structures.

Application of anisotropic function spaces to CR deformation analysis.

Enhanced understanding of the moduli space of CR structures.

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.