A Characterization of Ellipsoids

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 1991 English Publisher:Springer Science and Business Media LLCJournal:Results in Mathematics, volume 20, pages 657-659 (issn: 0378-6218, eissn: 1420-9012,

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Authors: Li, Anmin;

doi: 10.1007/bf03323202

A Characterization of Ellipsoids

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Abstract

It is proved that a (sufficiently smooth) closed convex hypersurface in \((n+1)\)-dimensional affine space must be an ellipsoid, if one of the elementary symmetric functions of the equiaffine principal curvatures is constant. Formerly this result was only known under the additional assumption, that the affine curvatures are everywhere positive.

Related Organizations

Technical University of Berlin
Germany
Sichuan University
China (People's Republic of)

Keywords

elementary symmetric functions, equiaffine curvatures, Affine differential geometry, ellipsoid

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