Article

Inexistence of non-product Hessian rank 1 affinely homogeneous hypersurfaces $H^n \subset \mathbb{R}^{n+1}$ in dimension $n \geqslant 5$

Merker J.

10.13108/2023-15-1-56

${\mathtt{Aff}}(\mathbb{R}^3)$

$1$

$S^2 \subset \mathbb{R}^3$

$H^n \subset \mathbb{R}^{n+1}$

$\big\{ u = F(x_1, \dots, x_n) \big\}$

$\big( F_{x_i x_j} \big)$

$1$

$n = 2, 3, 4, 5, 6, 7$

$n = 2, 3, 4$

$n = 2$

$n = 5, 6, 7$

$\mathbb{R}^m$

$2, 3, 4$

$n \geqslant 5$

$\big\{ u = F(x_1, \dots, x_n) \big\}$

${\mathtt{Aff}}(\mathbb{R}^{n+1})$

$\leqslant n+5$

$n \geqslant 2$