Hopf fibration: geodesics and distances
Differential Geometry
2015-05-20 v1
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 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.
Keywords
Cite
@article{arxiv.1009.4789,
title = {Hopf fibration: geodesics and distances},
author = {Der-Chen Chang and Irina Markina and Alexander Vasil'ev},
journal= {arXiv preprint arXiv:1009.4789},
year = {2015}
}
Comments
22 pages, 6 figures