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Journal Articles Kyushu Journal of Mathematics Year : 2014

Decomposable affine hypersurfaces


In affine differential geometry, Calabi discovered how to associate a new hyperbolic affine hypersphere with two hyperbolic affine hyperspheres. This was later generalized by Dillen and Vrancken in order to obtain a large class of examples of equiaffine homogeneous affine hypersurfaces. Note that the constructions defined above remain valid if one of the affine hyperspheres is a point. In this paper we consider the converse question: how can we determine, given properties of the difference tensor K and the affine shape operator S, whether a given hypersurface can be decomposed as a generalized Calabi product of an affine sphere and a point?
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Dates and versions

hal-03228108 , version 1 (17-05-2021)


  • HAL Id : hal-03228108 , version 1


Miroslava Antić, Franki Dillen, Kristof Schoels, Luc Vrancken. Decomposable affine hypersurfaces. Kyushu Journal of Mathematics, 2014, 68 (1), pp.93-103. ⟨hal-03228108⟩
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