Classification of simply-transitive Levi non-degenerate hypersurfaces in\n \ℂ³

2020/10/13 by Boris Doubrov, Doubrov, Boris, Joël Merker +3
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2010.06334

Abstract

Holomorphically homogeneous CR real hypersurfaces M³ \⊂ \ℂ²\nwere classified by 'Elie Cartan in 1932. In the next dimension, we complete\nthe classification of simply-transitive Levi non-degenerate hypersurfaces M⁵\n\⊂ \ℂ³ using a novel Lie algebraic approach independent of any\nearlier classifications of abstract Lie algebras. Central to our approach is a\nnew coordinate-free formula for the fundamental (complexified) quartic tensor.\nOur final result has a unique (Levi-indefinite) non-tubular model, for which we\ndemonstrate geometric relations to planar equi-affine geometry.\n

Related

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• Holomorphically Homogeneous Real Hypersurfaces in \mathbb C³
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