Classification of Simply-Transitive Levi Non-Degenerate Hypersurfaces in C^3

Joël Merker (1) , Boris Doubrov (2) , Dennis The (3)

1 LMO - Laboratoire de Mathématiques d'Orsay
2 Belarusian State University, Faculty of Mathematics and Mechanics
3 UiT - The Arctic University of Norway [Tromsø, Norway]

Holomorphically homogeneous CR real hypersurfaces M^3 in C^2 were classified by Élie Cartan in 1932. In the next dimension, we complete the classification of simply-transitive Levi nondegenerate hypersurfaces M^5 in 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.

Domaines: Mathématiques [math]

Joël Merker, Boris Doubrov, Dennis The. Classification of Simply-Transitive Levi Non-Degenerate Hypersurfaces in C^3. International Mathematics Research Notices, In press. ⟨hal-03286301⟩