Holonomy Displacements in Hopf Bundles over Complex Hyperbolic Space and the Complex Heisenberg Groups
نویسندگان
چکیده
For the “Hopf bundle” S → S → CH, horizontal lifts of simple closed curves are studied. Let γ be a piecewise smooth, simple closed curve on a complete totally geodesic surface S in the base space. Then the holonomy displacement along γ is given by V (γ) = e where A(γ) is the area of the region on the surface S surrounded by γ; λ = 1/2 or 0 depending on whether S is a complex submanifold or not. We also carry out a similar investigation for the complex Heisenberg group R → H → C.
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