Hopf fibration: Geodesics and distances |
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| Authors: | Der-Chen Chang,Irina Markina,Alexander Vasil&rsquo ev |
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| Affiliation: | 1. Department of Mathematics, Georgetown University, Washington, DC 20057, USA;2. Department of Mathematics, University of Bergen, P.O. Box 7803, Bergen N-5020, Norway |
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| Abstract: | Here we study geodesics connecting two given points on odd-dimensional spheres respecting the Hopf fibration. This geodesic boundary value problem is completely solved in the case of three-dimensional sphere and some partial results are obtained in the general case. The Carnot–Carathéodory distance is calculated. We also present some motivations related to quantum mechanics. |
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| Keywords: | primary 53C17 |
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