Hopf fibration: geodesics and distances
classification
🧮 math.DG
keywords
casefibrationgeodesicshopfsomeboundarycalculatedcarnot-carath
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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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