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Isotropic affine hypersurfaces of dimension 5

Abstract : We study affine hypersurfaces M which have isotropic difference tensor. Note that any surface always has isotropic difference tensor. Therefore, we may assume that n > 2. Such hypersurfaces have previously been studied by the first author and M. Djoric in [1] under the additional assumption that M is an affine hypersphere. Here we study the general case. As for affine spheres, we first show that isotropic affine hypersurfaces which are not congruent to quadrics are necessarily 5, 8, 14 or 26 dimensional. From this, we also obtain a complete classification in dimension 5.
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Submitted on : Tuesday, May 25, 2021 - 9:55:32 AM
Last modification on : Friday, March 4, 2022 - 1:51:22 PM

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Olivier Birembaux, Luc Vrancken. Isotropic affine hypersurfaces of dimension 5. Journal of Mathematical Analysis and Applications, Elsevier, 2014, 417 (2), pp.918-962. ⟨10.1016/j.jmaa.2014.03.071⟩. ⟨hal-03233808⟩

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