Emord Nila Palindrome wrote:
> It is certainly bad usage, for the following reason: the phrase,
> "the metric", implies that there is *one* metric function on
> Riemannian geometry, which is false. This reason has nothing
> to do with distance measure in general, as commonly understood,
> or otherwise.
Actually, there *is* essentially one canonical metric function on
Riemannian geometry. In either model of absolute geometry there is, up
to a multiplicative constant, only one metric preserved by reflection.
In hyperbolic geometry, moreover, there is an absolute distance scale
based on angular defect.
Obviously, you can put a different metric on the points of the
hyperbolic plane (or on any set); but this is a vacuous observation.
Only one metric is actually a metric for the plane rather than its
underlying set.
-Robert Dawson
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
