Qualitative properties of CR-structures

Abstract

Let M be a $C^{\infty}$ manifold of any dimension ≥ 1. A CR-structure on M is the datum of a formally integrable vector subbundle T of CTM, complex tangent bundle, satisfying the following condition. $T \cap \bar{T} = 0$ The CR-structure T is a complex structure if and only if $T\oplus \bar{T} = CTM$ The purpose of this work is to study the generalization of the unique continuation property in CR-manifolds and the local integrability of CR-structures.