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Random spherical triangles I: Geometrical background

Published online by Cambridge University Press:  01 July 2016

Huiling Le
Huiling Le*
Affiliation:
University of Cambridge
*
∗ Postal address: Statistical Laboratory, 16 Mill Lane, Cambridge CB2 1SB, UK.
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Abstract

In this paper we identify the shape space Σ(S 2, k) for k labelled points on the sphere S 2 that gives a mathematical model applicable to data sets whose elements are, or can be represented by, configurations of labelled sequences of points on S2 and for which the fundamental properties of interest are the shapes of these configurations, and we examine the geometric structures on the space, especially the riemannian structure on Σ(S 2, 3). In a companion paper (pp. 581–594) we investigate the statistical properties of such shapes when the k points are generated by a random mechanism.

Keywords

COLLINEARITYCURVATUREGEODESIC DISTANCEPROCRUSTEAN METRICQUASARSRIEMANNIAN METRIC

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 21 , Issue 3 , September 1989 , pp. 570 - 580
Copyright
Copyright © Applied Probability Trust 1989 

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References

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