Another rigidity theorem for affine immersions (Q1895220)

A new affine version of the Beez-Killing theorem is proved. The first affine version proposed by the reviewer in [Monatsh. Math. 113, No. 3, 245-254 (1992; Zbl 0776.53007)], says that if \(a\) the type number of a hypersurface in \(\mathbb{R}^{n+ 1}\) is greater than 1 and the rank of the shape operator is greater than 2, then the hypersurface is rigid modulo the affine general group. In the version of this paper the hypersurface is assumed to be nondegenerate and its shape operator to have rank greater than 1.