https://universite-paris-saclay.hal.science/hal-03286301Merker, JoëlJoëlMerkerLMO - Laboratoire de Mathématiques d'Orsay - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueDoubrov, BorisBorisDoubrovBelarusian State University, Faculty of Mathematics and MechanicsThe, DennisDennisTheUiT - The Arctic University of Norway [Tromsø, Norway]Classification of Simply-Transitive Levi Non-Degenerate Hypersurfaces in C^3HAL CCSD2021[MATH] Mathematics [math]MERKER, Joël2021-07-14 10:55:322023-03-24 14:53:222021-07-19 08:51:03enJournal articlesapplication/pdf1Holomorphically 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.