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Angle Measures and Bisectors in Minkowski Planes

Published online by Cambridge University Press:  20 November 2018

Nico Düvelmeyer*
Affiliation:
Technische Universität Chemnitz, Fakultät für Mathematik, D-09107 Chemnitz, Germany e-mail: [email protected]
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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2005

References

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