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A Metric Inequality for the Thompson and Hilbert Geometries

Cormac Walsh·Roger D. Nussbaum
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Abstract

There are two natural metrics defined on an arbitrary convex cone: Thompson's part metric and Hilbert's projective metric. For both, we establish an inequality giving information about how far the metric is from being non-positively curved.

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Cormac Walsh, Roger D. Nussbaum. 2004-05-07. A Metric Inequality for the Thompson and Hilbert Geometries. https://arxiv.org/abs/math/0405130

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