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We demonstrate that a class of torus-shaped Hopf maps with arbitrary linkingnumber obeys the static complex eikonal equation. Further, we explore thegeometric structure behind these solutions, explaining thereby the reason fortheir existence. As this equation shows up as an integrability condition incertain non-linear field theories, the existence of such solutions is of someinterest.Comment: 13 pages, slight changes in presentation, one paragraph on the  symmetries of the eikonal equation added. Version accepted for publication in  JM

Hopf maps as static solutions of the complex eikonal equation