A supplement to the Alexandrov–Lester Theorem


Abstract


Let V be the 4-dimensional Minkowski-space of special relativity over the reals with quadratic form Q. Consider a mapping \psi:V→ V such that Q(x-y)=0\Leftrightarrow Q(x\psi-y\psi)=0 for all x,y \in V. Under the assumption that \psi is a bijection Alexandrov's theorem states that \psi is a linear bijection followed by a translation. Our results imply (as a special case) that the assumption of \psi being a bijection an be dropped.

DOI Code: 10.1285/i15900932v21n2p35

Keywords: Distance-preserving mappings; Collineations; Orthogonal groups; Special relativity

Classification: 51N30; 51F25; 83A05; 51M05; 51P05

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