HOLONOMY DISPLACEMENTS IN THE HOPF BUNDLES OVER CHn AND THE COMPLEX HEISENBERG GROUPS
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For the "Hopf bundle" S1 →S2n,1 → CHn, horizontal lifts of simple closed curves are studied. Let be a piecewise smooth, simple closed curve on a complete totally geodesic surface S in the base space. Then the holonomy displacement along is given by 수식 where A(γ) is the area of the region on the surface S surrounded byγ ;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 !→H2n+1 →Cn.
Abstract
For the "Hopf bundle" S1 →S2n,1 → CHn, horizontal lifts of simple closed curves are studied. Let be a piecewise smooth, simple closed curve on a complete totally geodesic surface S in the base space. Then the holonomy displacement along is given by 수식 where A(γ) is the area of the region on the surface S surrounded byγ ;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 !→H2n+1 →Cn.
참고문헌 (3)
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- J. Wolf, "Spaces of Constant Curvature, 5th ed" (1984), Publish or Perish