Parallel transport
Once more, we use the sphere to illustrate how parallel transport works (with the kernel).
The metric in (,
) coordinates is
The essential computation is carried out in line 1 of the following code. The command is ΧP[g,{t,h},{0,2 π}]. The input to ΧP is the metric g, a curve γ(t):I→M, and the interval I⊂R.
We plot parallel transport of an orthonormal frame along several meridians.
An animation is sampled by "AnimationDisplayTime".
Created by Mathematica (December 22, 2006) | ![]() |