Abstract
If a Hilbert geometry satisfies a rather weak version of either Ceva’s or Menelaus’ theorem for every triangle, then it is hyperbolic.
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Kozma, J., Kurusa, Á. Ceva’s and Menelaus’ theorems characterize the hyperbolic geometry among Hilbert geometries. J. Geom. 106, 465–470 (2015). https://doi.org/10.1007/s00022-014-0258-7
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DOI: https://doi.org/10.1007/s00022-014-0258-7