Abstract
By using a computer the following theorem is proved: Consider K=GF(q), q ε {32,64,81,128}, σ:K2 → K2 bijective such that\(\overline {PQ} = 1\) ⇒\(\overline {P^\sigma Q^\sigma } = 1\) ∀ P,Q ε K2. Then σ is a semi-isometry. The assumption bijective can be dropped if q ε {32,128}.
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Samaga, HJ. Über Abstand 1 erhaltende Abbildungen in Minkowski-Ebenen. J Geom 22, 183–188 (1984). https://doi.org/10.1007/BF01222843
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DOI: https://doi.org/10.1007/BF01222843