Canonical equiaffine hypersurfaces in \(\mathbb{R}^{n+1}\)
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.
scientific article; zbMATH DE number 567428
scientific article