| Type de publication : |
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Articles dans des revues avec comité de lecture |
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| Domaine : |
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Mathématiques/Géométrie différentielle
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| Titre : |
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Isometric Immersions of Hypersurfaces in 4-dimensional Manifolds via Spinors |
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| Auteur(s) : |
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Marie-Amélie Lawn ( ) 1, Julien Roth () 2 |
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| Laboratoire : |
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| Résumé : |
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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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Langue du texte
intégral : |
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Anglais |
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| Journal : |
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| Differential Geometry and its Applications |
| Publisher |
Elsevier |
| ISSN |
0926-2245 |
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| Audience : |
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internationale |
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| Date de publication : |
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01/04/2010 |
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| Volume : |
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28 |
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| Numéro : |
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2 |
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| Page, identifiant, ... : |
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205-219 |
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| Mots Clés : |
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Dirac Operator – Generalized Killing Spinors – Isometric Immersions – Gauss and Codazzi-Mainardi Equations – Energy-Momentum Tensor |
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| Classification : |
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53C27; 53C40; 53C80; 58C40 |
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| Commentaire : |
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21 pages, to appear in Differential Geometry and its Applications |
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