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) |