Moving frames and parallel transport

Parallel transport and the geometric phase

Python and matlab scripts to animate the moving frames:

• the tangent frame
• the darboux frame, and
• the frenet serret frame

and the parallel transport of a tangent vector, using the quaternions cited in reference 1).

Also animated are:

• the parallel transport of a 3-vector, and
• the geometric phase of a 2-vector.

The geometric phase is generalized to non-spherical surfaces. Surface options are:

• the 2-sphere, and
• bushings surfaces of revolution

Surfaces

References

• Brian O'Sullivan, ”The Hopf Fibration and Hidden Variables in Quantum and Classical Mechanics” April (2021) arXiv:1601.02569

• Bushings function (repository)