# On equivalence problem for 2--nondegenerate CR geometries with simple models

## TL;DR

This paper solves the equivalence problem for 2-nondegenerate CR geometries with simple models, completing the classification of maximally symmetric real submanifolds in complex space and constructing their local embeddings.

## Contribution

It provides a complete solution to the equivalence problem for these CR geometries with simple automorphism groups, including explicit local embeddings.

## Key findings

- Classification of maximally symmetric CR models completed
- Explicit local embeddings into complex space constructed
- Unified framework for equivalence problem of 2-nondegenerate CR geometries

## Abstract

In this article, we solve the equivalence problem for 2--nondegenerate CR geometries that have (at every point) a homogeneous space $G/H$ as a maximally symmetric model for $G$ simple real Lie group of CR automorphisms. This completes the classification of real submanifolds in complex space that are maximally symmetric models with a real simple CR automorphism group. In particular, we construct (local) embeddings of these models into complex space.