A small vector is parallel-transported once around a latitude circle at colatitude on…
PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Tensors and differential geometry · Tensors and differential geometry
Invariance, Ch Curvature
Problem
A small vector is parallel-transported once around a latitude circle at colatitude θ0=30∘ on a sphere of radius a (colatitude is measured from the north pole, so θ0=0 is the pole and θ0=90∘ is the equator). Using the result that the holonomy of a loop on the sphere equals the enclosed area divided by a2, find the angle by which the vector is rotated relative to its own starting direction after one circuit.