2 problems

Let $F$ be a Minkowski norm on $\mathbb{R}^n$ with Hessian metric $g$, where $n\geq 3$. Laugwitz's conjecture. If $g$ is flat on $\mathbb{R}^n\backslash\{0\}$, then $F$ is Euclidea…

Finiteness conjecture. The class of all such submetries contains only finitely many foliated homeomorphism types.