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| HAL : hal-00264969, version 2 |
| arXiv : 0803.2621 |
| Fiche détaillée |  Récupérer au format |
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| Differential Geometry and its Applications 28, 2 (2010) 205-219 |
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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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| (01/04/2010) |
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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. As an application, we deduce a non-existence result for hypersurfaces in the 4-dimensional Euclidean space. |
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| 1 : | Unité de recherche en mathématiques |
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Université de Luxembourg |
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| 2 : | Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA) |
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Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8050 – Fédération de Recherche Bézout |
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| Domaine | : | Mathématiques/Géométrie différentielle |
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| Dirac Operator – Generalized Killing Spinors – Isometric Immersions – Gauss and Codazzi-Mainardi Equations – Energy-Momentum Tensor |
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| hal-00264969, version 2 | |
| http://hal.archives-ouvertes.fr/hal-00264969 | |
| oai:hal.archives-ouvertes.fr:hal-00264969 | |
| Contributeur : Julien Roth | |
| Soumis le : Mardi 9 Décembre 2008, 15:49:26 | |
| Dernière modification le : Vendredi 10 Septembre 2010, 16:26:34 | |
