On Angles and The Fundamental Theorems of Metric Geometry |
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Authors: | Burkhard Alpers |
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Institution: | 1. University of Saskatchewan, Saskatoon, Saskatchewan S7N 0W0, Canada
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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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