A geodesic triangle is drawn on a sphere of radius

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Tensors and differential geometry · Tensors and differential geometry

Invariance, Ch Curvature

Problem

A geodesic triangle is drawn on a sphere of radius aa, with interior angles 95∘95^\circ, 100∘100^\circ and 110∘110^\circ. A vector is parallel-transported once around the triangle. Find the angle by which the vector is rotated relative to its own starting direction, using the local Gauss-Bonnet theorem ∑αi−π=∫K dA\sum\alpha_i - \pi = \int K\,\mathrm{d}A and the fact that this integral equals the loop's holonomy.

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