Hopf fibration: geodesics and distances

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-Carathéodory distance is calculated. We also present some motivations related to quantum mechanics.

22 pages, 6 figures

References in corpus (1)

• Sub-Riemannian geodesics and heat operator on odd dimensional spheres

Cited by in corpus (5)

• Spectral multipliers for the Kohn Laplacian on forms on the sphere in ${\mathbb{C}}^n$
• Unitary symmetries in wormhole geometry and its thermodynamics
• The Length Spectrum of the Sub-Riemannian Three-Sphere
• Length spectra of sub-Riemannian metrics on compact Lie groups
• A note on sub-Riemannian structures associated with complex Hopf fibrations