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Angle Measures and Bisectors in Minkowski Planes

Published online by Cambridge University Press:  20 November 2018

Nico Düvelmeyer
Nico Düvelmeyer*
Affiliation:
Technische Universität Chemnitz, Fakultät für Mathematik, D-09107 Chemnitz, Germany e-mail: nico.duevelmeyer@mathematik.tu-chemnitz.de
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Abstract

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We prove that a Minkowski plane is Euclidean if and only if Busemann's or Glogovskij's definitions of angular bisectors coincide with a bisector defined by an angular measure in the sense of Brass. In addition, bisectors defined by the area measure coincide with bisectors defined by the circumference (arc length) measure if and only if the unit circle is an equiframed curve.

Keywords

52A1052A21Radon curvesMinkowski geometryMinkowski planesangular bisectorangular measureequiframed curves
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 4 , 01 December 2005 , pp. 523 - 534
Copyright
Copyright © Canadian Mathematical Society 2005

References

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