On a general principle in geometry that leads to functional equations

DOI10.1007/BF01833993zbMath0788.39005MaRDI QIDQ1312254

Walter Benz

Publication date: 26 May 1994

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/137535

zbMATH Keywords

fieldsareageometriesinvariantsdistanceanglefunctional equationssurvey papers

Mathematics Subject Classification ID

Hyperbolic and elliptic geometries (general) and generalizations (51M10) Functional equations for real functions (39B22) Functional equations for functions with more general domains and/or ranges (39B52) Research exposition (monographs, survey articles) pertaining to difference and functional equations (39-02) Euclidean geometries (general) and generalizations (51M05) Orthogonal and unitary groups in metric geometry (51F25) Analytic geometry with other transformation groups (51N25)

Cites Work

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• Note on angle-preserving mappings
• On distance-preserving transformations of lines in Euclidean three-space
• A characterization of the semi-isometries of a Minkowski plane over a field K
• Martin's theorem for Euclidean n-space and a generalization to the perimeter case
• Über einen Satz von June Lester zur Charakterisierung Euklidischer Bewegungen. (On a theorem of J. Lester about the characterization of Euclidean motions)
• Maps which almost preserve angles
• Eine Beckman-Quarles-Charakterisierung der Lorentztransformationen des \(\mathbb{R}^n\)
• The Beckman-Quarles theorem in Minkowski space for a spacelike square- distance
• Der Satz von Benz-Rado. (The theorem of Benz-Rado)
• On Isometries of Euclidean Spaces

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