A characterization of hyperbolic geometry among Hilbert geometry (Q1021290)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A characterization of hyperbolic geometry among Hilbert geometry |
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A characterization of hyperbolic geometry among Hilbert geometry (English)
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8 June 2009
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The space of Hilbert geometry is the analogue of the projective model of hyperbolic space where the ellipsoid is replaced by an arbitrary convex body \(K\). It is shown that \(K\) is an ellipsoid if the three medians of any triangle always meet in one point, thus getting a characterization of hyperbolic space. It suffices to do this in two dimensions.
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hyperbolic geometry
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Hilbert geometry
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triangle
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ellipsoid
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