Geodesic
Conformal and elliptic models of Hopf bundle
Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 24 (2003), pp. 81-98
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The Hopf bundle $\pi\colon S^{2n+1}\to\mathbb{CP}^n$ is one of the most famous examples of nontrivial principal bundles. In this paper we consider two models of this bundle for $n=1$. The first (conformal) model is obtained by the stereographic mapping of $S^3$ onto the conformal space, the second one is constructed with the use of the standard two-sheeted covering $S^3\to\mathbb{B}^3$ of the elliptic space. We find the bundle connection in these models and find the curvature of this connection. The results of the first two sections are obtained by I. A. Kuzmina, the third part is written by B. N. Shapukov. 
@article{KUTGS_2003_24_a8,
     author = {I. A. Kuz'mina and B. N. Shapukov},
     title = {Conformal and elliptic models of {Hopf} bundle},
     journal = {Trudy Geometricheskogo Seminara},
     pages = {81--98},
     year = {2003},
     volume = {24},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/KUTGS_2003_24_a8/}
}
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I. A. Kuz'mina; B. N. Shapukov. Conformal and elliptic models of Hopf bundle. Trudy Geometricheskogo Seminara, Trudy Geometricheskogo Seminara, Tome 24 (2003), pp. 81-98. http://geodesic.mathdoc.fr/item/KUTGS_2003_24_a8/