A supplement to the Alexandrov–Lester Theorem
Abstract
Let be the 4-dimensional Minkowski-space of special relativity over the reals with quadratic form Q. Consider a mapping such that for all . Under the assumption that is a bijection Alexandrov's theorem states that is a linear bijection followed by a translation. Our results imply (as a special case) that the assumption of 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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