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| HAL : hal-00264969, version 1 |
| arXiv : 0803.2621 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (18-03-2008) | v2 (09-12-2008) |
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| Isometric Immersions of Hypersurfaces in 4-dimensional Manifolds via Spinors |
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| Marie-Amélie Lawn 1Julien Roth 2 |
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| (18/03/2008) |
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| We give a spinorial characterization of isometrically immersed hypersurfaces into 4-dimensional space forms and product spaces $\M^3(\kappa)\times\R$, in terms of the existence of particular spinor fields, called generalized Killing spinors or equivalently solutions of a Dirac equation. This generalizes to higher dimensions several recent results for surfaces by T.\,Friedrich, B.\,Morel and the two authors. The main argument is the interpretation of the energy-momentum tensor of a generalized Killing spinor as the second fundamental form, possibly up to a tensor depending on the ambient space. |
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| 1 : | Unité de recherche en mathématiques |
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Université de Luxembourg |
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| 2 : | Laboratoire Jean Alexandre Dieudonné (JAD) |
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CNRS : UMR6621 – Université Nice Sophia Antipolis [UNS] |
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| Domaine | : | Mathématiques/Géométrie différentielle |
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| Dirac Operator – Generalized Killing Spinors – Isometric Immersions – Gauss and Codazzi-Mainardi Equations |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00264969, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00264969 | |
| oai:hal.archives-ouvertes.fr:hal-00264969 | |
| Contributeur : Julien Roth | |
| Soumis le : Mardi 18 Mars 2008, 13:56:23 | |
| Dernière modification le : Mardi 18 Mars 2008, 14:00:46 | |
