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Characterization of the generalized Calabi composition of affine hyperspheres

Abstract : In this paper, continuing with Hu-Li-Vrancken and the recent work of Antie-Dillen-Schoels Vrancken, we obtain a decomposition theorem which settled the problem of how to determine whether a given locally strongly convex affine hypersurface can be decomposed as a generalized Calabi composition of two affine hyperspheres, based on the properties of its difference tensor K and its affine shape operator S.
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Submitted on : Tuesday, May 25, 2021 - 9:16:37 AM
Last modification on : Wednesday, February 16, 2022 - 11:46:06 AM

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M. Antic, Z. Hu, C. C. Li, Luc Vrancken. Characterization of the generalized Calabi composition of affine hyperspheres. Acta Mathematicae Applicatae Sinica, Springer Verlag, 2015, 31 (10), pp.1531-1554. ⟨10.1007/s10114-015-4431-1⟩. ⟨hal-03233620⟩

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