Normal forms in Cauchy-Riemann Geometry: a survey

TL;DR

This survey reviews the use of normal form techniques in CR-geometry to address the equivalence problem and describe moduli spaces of real submanifolds in complex space, highlighting key constructions and open challenges.

Contribution

It summarizes existing normal form methods in CR-geometry and presents open problems, providing a comprehensive overview of the field.

Findings

Normal form methods are effective for CR-geometry equivalence problems.

The survey identifies key normal form constructions in CR-geometry.

Several open problems in the field are formulated for future research.

Abstract

One of effective ways to solve the equivalence problem and describe moduli spaces for real submanifolds in complex space is the normal form approach. In this survey, we outline some normal form constructions in CR-geometry and formulate a number of open problems.