Hopf fibration: geodesics and distances

Details Hopf fibration: geodesics and distances Hopf fibration: geodesics and distances

2010-09-24

arxiv.org/abs/1009.4789v1

Mathematics

Differential Geometry

22 pages, 6 figures

Scientific paper

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 3-dimensional sphere and some partial results
are obtained in the general case. The Carnot-Carath\'eodory distance is
calculated. We also present some motivations related to quantum mechanics.

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