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Journal Articles International Mathematics Research Notices Year : 2021

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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Dates and versions

hal-03286301 , version 1 (14-07-2021)

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Boris Doubrov, Joël Merker, Dennis The. Classification of Simply-Transitive Levi Non-Degenerate Hypersurfaces in C^3. International Mathematics Research Notices, 2021, 2022 (19), pp.15421-15473. ⟨10.1093/imrn/rnab147⟩. ⟨hal-03286301⟩
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