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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 or...der 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?続きを見る
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Mendeley出力
