Homogeneous CR-manifold in $\mathbb{C}^4$

TL;DR

This paper classifies holomorphically homogeneous CR-type submanifolds in complex 4-space, identifying a unique model surface with this property and analyzing its automorphism group and orbit structure.

Contribution

It introduces a classification of homogeneous CR-model surfaces in a7^4, including the unique homogeneous model and its automorphism group.

Findings

Existence of a unique holomorphically homogeneous model surface.

Description of the moduli space of CR-model surfaces.

Classification of orbits under the automorphism group.

Abstract

In this paper we study holomorphically homogeneous model submanifolds CR-type (1, 3) complex space $\mathbb C^4$. One finds moduli space of five-dimensional model surfaces Bloom-Graham type ((2, 1), (3, 1), (4, 1)). It is shown that there exists unique model surface of this type with property of holomorphical homogeneous, which is equivalent to tube surface $\mathcal C$ with affin homogeneous base. One describes and classifies with respect to model surfaces the orbits relative to the group of holomorhical automorphisms of $\mathcal C$