Holomorphically Homogeneous Real Hypersurfaces in $\mathbb C^3$
Abstract
We give a complete description and classification of locally homogeneous real hypersurfaces in . Various groups of mathematicians have been studying this problem in the last 25 years, and several significant classes of hypersurfaces under consideration have been studied and classified. The final results in the classification problem presented in this paper are obtained by using the classification of abstract 5-dimensional real Lie algebras, and by studying their representations by algebras of holomorphic vector fields in complex 3-space. The complete list of pairwise inequivalent hypersurfaces that we obtain contains 47 types of homogeneous hypersurfaces; some of the types are 1- or 2-parametric families, and each of the others is single hypersurface or a finite family of hypersurface.
Keywords
Cite
@article{arxiv.2006.07835,
title = {Holomorphically Homogeneous Real Hypersurfaces in $\mathbb C^3$},
author = {A. V. Loboda},
journal= {arXiv preprint arXiv:2006.07835},
year = {2020}
}
Comments
This paper is to appear in the Proceeding of the Moscow Mathematical Society ("Trudy Moskovskogo Matematicheskogo Obshchestva"); it was submitted to the journal in March 2020. The current version is the original Russian one, and the English version is to appear soon. The complete classification of locally homogeneous hypersurfaces in $\mathbb C^3$ is given on pages 53-54