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Four-dimensional locally strongly convex homogeneous affine hypersurfaces

Abstract : We study four-dimensional locally strongly convex, locally homogeneous, hypersurfaces whose affine shape operator has two distinct principal curvatures. In case that one of the eigenvalues has dimension 1 these hypersurfaces have been previously studied in Dillen and Vrancken (Math Z 212:61–72, 1993, J Math Soc Jpn 46:477–502, 1994) and Hu et al. (Differ Geom Appl 33:46–74, 2014) in which a classification of such submanifolds was obtained in dimension 4 and 5 under the additional assumption that the multiplicity of one of the eigenvalues is 1. In this paper we complete the classification in dimension 4 by considering the case that the multiplicity of both eigenvalues is 2.
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Submitted on : Friday, February 19, 2021 - 10:21:32 AM
Last modification on : Tuesday, October 19, 2021 - 11:38:45 AM

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Abdelouahab Chikh Salah, Luc Vrancken. Four-dimensional locally strongly convex homogeneous affine hypersurfaces. Journal of Geometry, Springer Verlag, 2017, 108 (1), pp.119-147. ⟨10.1007/s00022-016-0330-6⟩. ⟨hal-03146492⟩

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