Canonical equiaffine hypersurfaces in \(\mathbb{R}^{n+1}\) (Q1323428)
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scientific article; zbMATH DE number 567428
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Canonical equiaffine hypersurfaces in \(\mathbb{R}^{n+1}\) |
scientific article; zbMATH DE number 567428 |
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Canonical equiaffine hypersurfaces in \(\mathbb{R}^{n+1}\) (English)
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10 May 1994
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The author defines a canonical hypersurface in real affine space by two conditions: (i) the Blaschke metric is flat, (ii) the cubic form is parallel to the Blaschke metric. Such a hypersurface, in particular, is an affine hypersphere. In case that the index of the Blaschke metric is one, Wang gives a complete classification of canonical hypersurfaces. The method of proof is very interesting: The author reduces this characterization to an algebraic classification problem for commutative, selfadjoint linear operators in a Lorentzian vector space. These operators are defined via the cubic form.
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Blaschke metric
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cubic form
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affine hypersphere
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