2020/06/14 by А. В. Лобода, Loboda, A. V.
Mathematics · #Advanced Topics in Algebra #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2006.07835
openalex publication_date 2020/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a complete description and classification of locally homogeneous real hypersurfaces in \mathbb C3. 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.