Published online by Cambridge University Press: 20 January 2009
Several papers on the subject of spatial distance in General Relativity appeared a few years ago, and a simple extension of this idea to any pair of points in any Riemannian space was given by me in a thesis. A distance invariant was defined, and this was found to depend upon a certain two-point invariant which was first introduced by H. S. Ruse in a study of Laplace's Equation. This invariant, now written ρ and defined in (3), has lately re-appeared, and it may now be of interest to publish the results found earlier. These include a geometrical interpretation of ρ, a simple method of calculation, and an expansion as a power series in the geodesic arc. The dependence of ρ upon the geodesic arc is also considered.
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