Crofton formulae and geodesic distance in hyperbolic spaces
Functional Analysis
2013-02-26 v1
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.
Cite
@article{arxiv.1302.5790,
title = {Crofton formulae and geodesic distance in hyperbolic spaces},
author = {Guyan Robertson},
journal= {arXiv preprint arXiv:1302.5790},
year = {2013}
}