Abstract.
The energy of an oriented q-distribution ? in a compact oriented manifold M is defined to be the energy of the section of the Grassmannian manifold of oriented q-planes in M induced by ?. In the Grassmannian, the Sasaki metric is considered. We show here a condition for a distribution to be a critical point of the energy functional. In the spheres, we see that Hopf fibrations are critical points. Later, we prove the instability for these fibrations.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
(Received 30 December 2000; in revised form 11 April 2001)
Rights and permissions
About this article
Cite this article
Chacón, P., Naveira, A. & Weston, J. On the Energy of Distributions, with Application to the Quaternionic Hopf Fibrations. Mh Math 133, 281–294 (2001). https://doi.org/10.1007/PL00010092
Issue Date:
DOI: https://doi.org/10.1007/PL00010092