On the Minkowski Problem in Affine Geometry

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 1991 English Publisher:Springer Science and Business Media LLCJournal:Results in Mathematics, volume 20, pages 643-649 (issn: 0378-6218, eissn: 1420-9012,

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Authors: Kurose, Takashi;

doi: 10.1007/bf03323200

On the Minkowski Problem in Affine Geometry

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Abstract

Using the solution of the \(n\)-dimensional Minkowski problem due to \textit{S.-Y. Cheng} and \textit{S. T. Yau} [Commun. Pure Appl. Math. 29, 495-516 (1976; Zbl 0363.53030)], the author obtains an analog of this result in equiaffine differential geometry. The essential idea is to express equiaffine invariants in terms of Euclidean invariants, as in \textit{W. Blaschke}, Vorlesungen über Differentialgeometrie. II. Affine Differentialgeometrie (Springer, Berlin 1923), \S 64.

Related Organizations

Fukuoka University
Japan
Fukuoka University
Japan

Keywords

equiaffine differential geometry, Affine differential geometry, Minkowski problem

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