Hopf maps as static solutions of the complex eikonal equation
Mathematical Physics
2009-11-10 v2 High Energy Physics - Theory
math.MP
Abstract
We demonstrate that a class of torus-shaped Hopf maps with arbitrary linking number obeys the static complex eikonal equation. Further, we explore the geometric structure behind these solutions, explaining thereby the reason for their existence. As this equation shows up as an integrability condition in certain non-linear field theories, the existence of such solutions is of some interest.
Keywords
Cite
@article{arxiv.math-ph/0312031,
title = {Hopf maps as static solutions of the complex eikonal equation},
author = {C. Adam},
journal= {arXiv preprint arXiv:math-ph/0312031},
year = {2009}
}
Comments
13 pages, slight changes in presentation, one paragraph on the symmetries of the eikonal equation added. Version accepted for publication in JMP