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Spinorial representation of surfaces into 4-dimensional space forms |
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| Authors: | Pierre Bayard Marie-Amélie Lawn Julien Roth |
| Affiliation: | 1. Instituto de Fisica Y Matematicas, Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria, C-3 C.P. 58040, Morelia, Michoacan, MEXICO 2. UT Austin, Austin, USA 3. Department of Mathematics, 1 University Station C1200, Austin, TX, 78712-0257, USA 4. Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050), Université Paris-Est Marne-la-Vallée Cité Descartes, Batiment Copernic, Bureau 4B097 5, boulevard Descartes, Champs sur Marne, 77454, Marne-la-vallée cedex 2, France |
| Abstract: | In this paper we give a geometrically invariant spinorial representation of surfaces in four-dimensional space forms. In the Euclidean space, we obtain a representation formula which generalizes the Weierstrass representation formula of minimal surfaces. We also obtain as particular cases the spinorial characterizations of surfaces in $mathbb R ^3$ and in $S^3$ given by Friedrich and by Morel. |
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