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On Angles and The Fundamental Theorems of Metric Geometry

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Abstract

In this paper we investigate the abstract angle measure for affine metric spaces. Common features and differences between orthogonal angles and angles with measure ≠ 0 are examined. It turns out that an affine collineation which maps angles with a certain fixed measure α ≠ 0,4 to angles with another fixed measure β is already a metric collineation in nearly all cases (fundamental theorem). An analogous result is stated for projective metric spaces. Some applications concerning minimal conditions for metric collineations are given.

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Authors and Affiliations

  1. University of Saskatchewan, Saskatoon, Saskatchewan S7N 0W0, Canada

    Burkhard Alpers

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  1. Burkhard Alpers
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This article was written during the author’s stay as a postdoctoral fellow at the University of Saskatchewan in Saskatoon. The author would like to thank this institution, in particular Prof. Marshall, for the hospitality and the inspiring atmosphere.

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Alpers, B. On Angles and The Fundamental Theorems of Metric Geometry. Results. Math. 17, 15–26 (1990). https://doi.org/10.1007/BF03322626

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  • DOI: https://doi.org/10.1007/BF03322626

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