HOLONOMY DISPLACEMENTS IN THE HOPF BUNDLES OVER Hn AND THE COMPLEX HEISENBERG GROUPS Choi, Young-Gi; Lee, Kyung-Bai;
For the "Hopf bundle" , horizontal lifts of simple closed curves are studied. Let be a piecewise smooth, simple closed curve on a complete totally geodesic surface in the base space. Then the holonomy displacement along is given by where is the area of the region on the surface surrounded by ; or 0 depending on whether is a complex submanifold or not. We also carry out a similar investigation for the complex Heisenberg group .
The topological aspect of the holonomy displacement on the principal U(n) bundles over Grassmannian manifolds, Topology and its Applications, 2015, 196, 8
S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vol. II, Reprint of the 1969 original. Wiley Classics Library, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996.
U. Pinkall, Hopf tori in $S^3$, Invent. Math. 81 (1985), no. 2, 379-386.
J. Wolf, Spaces of Constant Curvature, 5th ed., Publish or Perish, Wilmington, 1984.