Hopf maps as static solutions of the complex eikonal equation

Details Hopf maps as static solutions of the complex eikonal equation Hopf maps as static solutions of the complex eikonal equation

2003-12-10

arxiv.org/abs/math-ph/0312031v2

J.Math.Phys. 45 (2004) 4017-4024

Physics

Mathematical Physics

13 pages, slight changes in presentation, one paragraph on the symmetries of the eikonal equation added. Version accepted for

Scientific paper

10.1063/1.1792931

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.

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