Infinitesimal and local rigidity of mappings of CR manifolds

TL;DR

This paper investigates the conditions under which holomorphic mappings between CR manifolds are locally rigid, reducing the problem to linear conditions and exploring automorphism group actions.

Contribution

It introduces sufficient infinitesimal criteria for local rigidity of CR mappings and analyzes the automorphism group's topological properties on the space of mappings.

Findings

Provided linearized conditions for local rigidity

Analyzed automorphism group actions on mapping spaces

Connected infinitesimal conditions to topological properties

Abstract

A holomorphic mapping $H$ between two real-analytic CR manifolds $M$ and $M'$ is said to be locally rigid if any other holomorphic map $F\colon M \to M'$ which is close enough to $H$ is obtained by composing $H$ with suitable automorphisms of $M$ and $M'$. 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 $M'$.