Classification of Simply-Transitive Levi Non-Degenerate Hypersurfaces in ℂ3. (24th June 2021)

• Record Type: Journal Article
• Authors: Doubrov, Boris; Merker, Joël; The, Dennis
• Is Part Of: International mathematics research notices. Volume 2022:Number 19(2022)
• Page Start: 15421
• Page End: 15473
• Publication Date: 2021-06-24
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnab147
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: Holomorphically homogeneous Cauchy–Riemann (CR) real hypersurfaces $M^3 \subset \mathbb{C}^2$ were classified by Élie Cartan in 1932. In the next dimension, we complete the classification of simply-transitive Levi non-degenerate hypersurfaces $M^5 \subset \mathbb{C}^3$ using a novel Lie algebraic approach independent of any earlier classifications of abstract Lie algebras. Central to our approach is a new coordinate-free formula for the fundamental (complexified) quartic tensor. Our final result has a unique (Levi-indefinite) non-tubular model, for which we demonstrate geometric relations to planar equi-affine geometry.