Analyticit\'e des applications CR dans des vari\'et\'es presque complexes

TL;DR

This paper investigates the real analyticity of CR mappings on specific hypersurfaces in almost complex manifolds, utilizing prolongation methods and complete systems to establish conditions for analyticity.

Contribution

It introduces a method of prolongation for tangential Cauchy-Riemann equations and proves real analyticity of CR mappings under certain deformation conditions of the almost complex structure.

Findings

CR mappings are real analytic when the codomain's almost complex structure is a deformation of a model structure.

The method of prolongation effectively analyzes the analyticity of CR mappings.

Conditions on the defining function of the hypersurface ensure analyticity in the almost complex setting.

Abstract

We study the real analyticity of a CR mapping on the hypersurface $\h$ defined by $\h=\{z\in\C^n,\Re(z_n)+|z'|^2=0\}$ in model almost complex manifolds. We make use of a method of prolongation for the tangential Cauchy-Riemann equations and a result about complete systems. We also prove that a CR mapping is real analytic when the almost complex structure of the codomain is a deformation of a model structure and the function defining the hypersurface in the codomain has a particular form.