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arXiv · 1302.5790

Crofton formulae and geodesic distance in hyperbolic spaces

Guyan Robertson
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Abstract

The geodesic distance between points in real hyperbolic space is a hypermetric, and hence is a kernel negative type. The proof given here uses an integral formula for geodesic distance, in terms of a measure on the space of hyperplanes. An analogous integral formula, involving the space of horospheres, is given for complex hyperbolic space.By contrast geodesic distance in a projective space is not of negative type.

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Guyan Robertson. 2013-02-23. Crofton formulae and geodesic distance in hyperbolic spaces. https://arxiv.org/abs/1302.5790

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