# Sufficient and necessary conditions for local rigidity of CR mappings and higher order infinitesimal deformations

## TL;DR

This paper investigates conditions under which CR mappings between minimal CR manifolds are locally rigid, introducing linear and higher order infinitesimal criteria to characterize this rigidity.

## Contribution

It provides new linear and higher order infinitesimal conditions that characterize local rigidity of CR mappings between minimal CR manifolds.

## Key findings

- Linear sufficient condition for local rigidity
- Higher order infinitesimal conditions characterize rigidity
- Applicable to finitely nondegenerate maps

## Abstract

In this paper we continue our study of local rigidity for maps of CR submanifolds of the complex space. We provide a linear sufficient condition for local rigidity of finitely nondegenerate maps between minimal CR manifolds. Furthermore, we show higher order infinitesimal conditions can be used to give a characterization of local rigidity.