Hopf fibration: Geodesics and distances

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Chang, Der-Chen²  Markina, Irina¹  Vasil'ev, Alexander¹ 

[1] Univ Bergen, Dept Math, N-5020 Bergen, Norway

[2] Georgetown Univ, Dept Math, Washington, DC 20057 USA

关键词: Sub-Riemannian geometry;    Hopf fibration;    Geodesic;    Carnot-Caratheodory distance;    Quantum state;    Bloch sphere;   

DOI  :  10.1016/j.geomphys.2011.01.011

来源: Elsevier

【 摘 要 】

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-Caratheodory distance is calculated. We also present some motivations related to quantum mechanics. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free