Equivalences of 5-dimensional CR manifolds III: Six models and elementary normalizations

TL;DR

This paper demonstrates that six nondegeneracy conditions for six classes of 5-dimensional CR manifolds can be directly read from their normalized defining equations, simplifying the analysis without advanced Moser theory.

Contribution

It provides a straightforward method to identify nondegeneracy conditions from normalized equations, avoiding complex Moser theory techniques.

Findings

Six nondegeneracy conditions are explicitly readable from normalized equations.

Each of the six classes has a unique set of elementary normalizations.

Simplifies the analysis of 5-dimensional CR manifolds by eliminating the need for advanced theory.

Abstract

The six nondegeneracy conditions of geometric nature that are satisfied by the only six possibly existing nondegenerate general classes I, II, III-1, III-2, IV-1, IV-2 of 5-dimensional CR manifolds are shown to be readable instantaneously from their elementarily normalized respective defining graphed equations, without advanced Moser theory.