Fiber Bundle Holonomy & Curvature

Parallel transport of a vector around a closed loop on a curved sphere. The holonomy angle equals the solid angle enclosed — a manifestation of curvature as the failure of parallel transport to return to itself.

Loop latitude θ

40°
Loop radius φ

90°
Speed

1.0×
Solid angle Ω:

Holonomy angle:

Berry phase γ: