Reduction of Five-Dimensional Uniformly Levi Degenerate CR Structures to Absolute Parallelisms

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 fact. Our result is the first instance of reduction to absolute parallelisms for Levi degenerate CR-structures.