Infinitesimal and local rigidity of mappings of CR manifolds

Abstract

A holomorphic mapping $H$ between two real-analytic CR manifolds $M$ and $M^{\prime }$ is said to be locally rigid if any other holomorphic map $F:M\to M^{\prime }$ which is close enough to $H$ is obtained by composing $H$ with suitable automorphisms of $M$ and $M^{\prime }$. With the aim of reducing the local rigidity problem to a linear one, we provide sufficient infinitesimal conditions. Furthermore we study some topological properties of the action of the automorphism group on the space of nondegenerate mappings from $M$ to $M^{\prime }$.