CR-manifolds of dimension 5: A Lie algebra approach

TL;DR

This paper investigates 5-dimensional CR-manifolds with transitive automorphism groups, providing examples, computing their automorphism groups, and analyzing the CR-function separability, revealing a common local CR-equivalence to the tube over the future light cone.

Contribution

It introduces a Lie algebra approach to classify and analyze 5-dimensional CR-manifolds with transitive automorphism groups, including explicit examples and their properties.

Findings

Examples are locally CR-equivalent to the tube over the future light cone.

Computed automorphism groups for the classes of hypersurfaces.

Identified maximal subsets not separable by global CR-functions.

Abstract

We study real-analytic Levi degenerate hypersurfaces M in complex manifolds of dimension 3, for which the CR-automorphism group Aut(M) is a real Lie group acting transitively on M. We provide large classes of examples for such M, compute the corresponding groups Aut(M) and determine the maximal subsets of M that cannot be separated by global continuous CR-functions. It turns out that all our examples, although partly arising in different contexts, are locally CR-equivalent to the tube over the future light cone in 3-dimensional space-time.