On nondegeneracy conditions for the Levi map in higher codimension: a survey

TL;DR

This survey compares different nondegeneracy conditions of the Levi map for higher codimension real submanifolds and explores their implications for biholomorphism determination, extending classical results to more complex settings.

Contribution

It systematically analyzes various nondegeneracy definitions and generalizes 2-jet biholomorphism determination to higher codimension cases.

Findings

Compared multiple nondegeneracy conditions of the Levi map

Extended 2-jet determination results to higher codimension

Provided a comprehensive survey of existing definitions and their relations

Abstract

We compare various definitions of nondegeneracy of the Levi map for real submanifolds of higher codimension in $C^N$ and discuss the generalization to higher codimension of the 2-jet determination for biholomorphisms in the hypersurface case proved by Chern and Moser.