多面体Hilbert几何的等距
Isometries of polyhedral Hilbert geometries
摘要：
我们证明了多面体希尔伯特几何的等距群与它的直射群（射影群）重合当且仅当多面体不是n-单形（n>=2）。此外，我们还确定了n维单形上Hilbert几何的等距群，并发现它有一个指数为2的直射变换群。这些结果证实了，对于多面体希尔伯特几何类，由P. de la Harpe提出的几个命题。
英文摘要：
We show that the isometry group of a polyhedral Hilbert geometry coincides with its group of collineations (projectivities) if and only if the polyhedron is not an n-simplex with n>=2. Moreover, we determine the isometry group of the Hilbert geometry on the n-simplex, and find that it has the collineation group as an index-two subgroup. These results confirm, for the class of polyhedral Hilbert geometries, several conjectures posed by P. de la Harpe.
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