论文标题
Laugwitz猜想和Landsberg Unicorn猜想的Minkowski规范，$ SO（K）\ Times So（N-K）$ - 对称性
Proof of Laugwitz Conjecture and Landsberg Unicorn Conjecture for Minkowski norms with $SO(k)\times SO(n-k)$-symmetry
论文作者
论文摘要
对于平滑的强烈凸出Minkowski Norm $ f：\ Mathbb {r}^n \ to \ Mathbb {r} _ {\ geq0} $，我们研究了与功能相对应的HESSIAN度量的等音，与该功能相对应$ e e = \ tfrac12f^2 $。在另外假设是$ f $相对于$ so（k）\ times so（n-k）$的标准操作是不变的，我们证明了1965年的Laugwitz的猜想。此外，我们描述了此类Hessian指标之间的所有等法线性$ so（k）\ times so（n-k）$ - 对称性
For a smooth strongly convex Minkowski norm $F:\mathbb{R}^n \to \mathbb{R}_{\geq0}$, we study isometries of the Hessian metric corresponding to the function $E=\tfrac12F^2$. Under the additional assumption that $F$ is invariant with respect to the standard action of $SO(k)\times SO(n-k)$, we prove a conjecture of Laugwitz stated in 1965. Further, we describe all isometries between such Hessian metrics, and prove Landsberg Unicorn Conjecture for Finsler manifolds of dimension $n\ge 3$ such that at every point the corresponding Minkowski norm has a linear $SO(k)\times SO(n-k)$-symmetry
