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

Abstract : 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.
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https://hal-universite-paris-saclay.archives-ouvertes.fr/hal-03286301
Contributor : Joël Merker Connect in order to contact the contributor
Submitted on : Wednesday, July 14, 2021 - 10:55:32 AM
Last modification on : Wednesday, July 21, 2021 - 3:47:17 AM
Long-term archiving on: : Friday, October 15, 2021 - 4:10:32 PM

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  • HAL Id : hal-03286301, version 1

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

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