Surfaces in S^3 and H^3 via Spinors

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We generalize the spinorial characterization of isometric immersions of surfaces in R^3 given by T. Friedrich (On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998)) to surfaces in S^3 and H^3. The main argument is the interpretation of the energy-momentum tensor associated with a special spinor field as a second fundamental form. It turns out that such a characterization of isometric immersions in terms of a special section of the spinor bundle also holds in the case of hypersurfaces in the Euclidean 4-space.
LaTeX, 12 pages

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Differential Geometry, 53C27, 53C45, 53A10

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http://salesiana.dossiersoluciones.com/handle/123456789/63740

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0204090
 http://arxiv.org/abs/math/0204090

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arXiv