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- W2085696903 abstract "For the Hopf bundle <TEX>$S^1{rightarrow}S^{2n,1}{rightarrow}mathbb{C}H^n$</TEX>, horizontal lifts of simple closed curves are studied. Let <TEX>${gamma}$</TEX> be a piecewise smooth, simple closed curve on a complete totally geodesic surface <TEX>$S$</TEX> in the base space. Then the holonomy displacement along <TEX>${gamma}$</TEX> is given by <TEX>$$V({gamma})=e^{{lambda}A({gamma})i}$$</TEX> where <TEX>$A({gamma})$</TEX> is the area of the region on the surface <TEX>$S$</TEX> surrounded by <TEX>${gamma}$</TEX>; <TEX>${lambda}=1/2$</TEX> or 0 depending on whether <TEX>$S$</TEX> is a complex submanifold or not. We also carry out a similar investigation for the complex Heisenberg group <TEX>$mathbb{R}{rightarrow}mathcal{H}^{2n+1}{rightarrow}mathbb{C}^n$</TEX>." @default.
- W2085696903 created "2016-06-24" @default.
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- W2085696903 date "2012-07-01" @default.
- W2085696903 modified "2023-10-01" @default.
- W2085696903 title "HOLONOMY DISPLACEMENTS IN THE HOPF BUNDLES OVER <TEX>$mathcal{C}$</TEX>HnAND THE COMPLEX HEISENBERG GROUPS" @default.
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- W2085696903 doi "https://doi.org/10.4134/jkms.2012.49.4.733" @default.
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