Explicit Construction of an Absolute Parallelism for Uniformly Levi-Degenerate 7-dimensional CR manifolds of hypersurface type

Abstract

This article is devoted to the local geometry of uniformly Levi-degenerate 2-nondegenerate CR manifolds of hypersurface type, particularly, the construction of explicit absolute paralellisms of such geometric objects in 7 dimensions with a constant CR symbol. Explicit constructions of such absolute parallelisms were given by Porter under additional symmetry properties and two of three cases arising from the signature of the Levi form. This article gives an explicit construction of the absolute parallelism of this last case using the bigraded prolongation given by Porter. It is also shown directly that the absolute parallelism does not give a Cartan connection. Show more