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Über einen Satz von June Lester zur Charakterisierung euklidischer Bewegungen

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Abstract

Let f: ℝn→ ℝn (3 <n <∞) be a mapping which preserves the area of equilateral triangles of side lengths 1,1,1. Then f is a euclidean motion. For n=3 the same holds if the area of triangles with side lengths 1,1,√3 is also preserved.

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Literaturhinweise

  1. F.S. BECKMAN, D.A. QUARLES: On Isometries of Euclidean Spaces. Proc. Amer. Math. Sec4, 810–815.

  2. P. GOUDERC, A. BALLINCIONI: Premier Livre du Tétraèdre, Paris 1953.

  3. J. LESTER: Martin's theorem for Euclidean n-Space and a generalization to the perimeter case. Journ. of Geometry27, 29–35, 1986.

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Authors and Affiliations

  1. II. Mathematisches Institut der Freien Universität Berlin, Arnimallee 3, D - 1000, Berlin 33

    Hanfried Lenz

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  1. Hanfried Lenz
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Herrn Prof. Otto Haupt zum 100. Geburtstag gewidmet

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Lenz, H. Über einen Satz von June Lester zur Charakterisierung euklidischer Bewegungen. J Geom 28, 197–201 (1987). https://doi.org/10.1007/BF01221944

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  • DOI: https://doi.org/10.1007/BF01221944

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