Author: Shmuel (Seymour J.) MetzShmuel (Seymour J.) Metz Date: Feb 21, 2007 15:28
>Parallel transport of a vector along a geodesic is defined by holding
>the angle of the vector constant along the geodesic.
Perhaps in a really old book. That's certainly not a contemporary
definition.
>Curvature is defined by parallel transporting a vector along a
>(small) loop and calculating the angle between the original and the
>transported vector.
C 'angle' 'difference'
>So, parallell transport and curvature depends heavily on the fact
>that we (me and the trouts?) are able to calculate angles.
No,
>Without a metric it makes no sense to talk about curvature.
Incorrect.
>Also parallel transport is meaningless in the absense of a metric.
Likewise incorrect.
>Instead of curvature we have torsion.
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