Reduction of five-dimensional uniformly Levi degenerate CR structures to absolute parallelisms

TL;DR

This paper demonstrates that a specific class of 5-dimensional CR structures can be reduced to absolute parallelisms valued in the Lie algebra so(3,2), facilitating their analysis and classification.

Contribution

It introduces a method to reduce 5-dimensional CR-hypersurfaces in class C_{2,1} to so(3,2)-valued absolute parallelisms, expanding tools for their study.

Findings

CR-structures in class C_{2,1} are reducible to absolute parallelisms

The reduction uses so(3,2)-valued structures

Applications of the reduction are provided

Abstract

Let ${\mathfrak C}_{2,1}$ be the class of connected 5-dimensional CR-hypersurfaces that are 2-nondegenerate and uniformly Levi degenerate of rank 1. We show that the CR-structures in ${\mathfrak C}_{2,1}$ are reducible to ${\mathfrak{so}}(3,2)$-valued absolute parallelisms and give applications of this result.