Figure 2
Illustration: Alan Stonebraker

Figure 2: Parallel transport of a vector on a curved surface, in this case a sphere. The transport takes place along geodesic segments (parts of great circles) forming a loop. The angle between the vector and each segment is constant (no local rotation). The final vector has been rotated compared to the initial one, the rotation angle being the solid angle enclosed by the loop. This “global rotation without local rotation” is the holonomy caused by the curvature of the sphere.