# The umbilical locus on the boundary of strictly pseudoconvex domains in $\mathbb C^2$

## TL;DR

This paper surveys recent results on the existence of umbilical points on three-dimensional CR submanifolds within strictly pseudoconvex domains in complex two-dimensional space, focusing on the Chern--Moser question.

## Contribution

It provides a comprehensive overview of recent advances related to the Chern--Moser problem on umbilical points in CR geometry.

## Key findings

- Summary of recent results on umbilical points
- Insights into the Chern--Moser question
- Open problems and future directions

## Abstract

The main objective of this paper is to survey some recent results on the Chern--Moser question concerning existence of umbilical points on three dimensional CR submanifolds in $\mathbb C^2$.