Hopf maps as static solutions of the complex eikonal equation | Zendy

C. Adam | Zendy

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Hopf maps as static solutions of the complex eikonal equation

Author(s) -

C. Adam

Publication year - 2004

Publication title -

journal of mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.708

H-Index - 119

eISSN - 1089-7658

pISSN - 0022-2488

DOI - 10.1063/1.1792931

Subject(s) - eikonal equation , mathematics , torus , class (philosophy) , field (mathematics) , mathematical analysis , eikonal approximation , evolution equation , pure mathematics , geometry , computer science , artificial intelligence

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

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