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| HAL : hal-00403620, version 1 |
| arXiv : 0907.1889 |
| Fiche détaillée |  Récupérer au format |
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| Gallot-Tanno theorem for closed incomplete pseudo-Riemannian manifolds and application. |
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| Pierre Mounoud 1 |
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| (10/07/2009) |
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| In this article we extend the Gallot-Tanno theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over such a manifold admits a parallel symmetric $2$-tensor then it is incomplete and has non zero constant curvature. An application of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics is given. |
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| 1 : | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| Domaine | : | Mathématiques/Géométrie différentielle |
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| cone manifold – parallel tensor – projective Lichnerowicz conjecture |
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| hal-00403620, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00403620 | |
| oai:hal.archives-ouvertes.fr:hal-00403620 | |
| Contributeur : Pierre Mounoud | |
| Soumis le : Vendredi 10 Juillet 2009, 16:51:33 | |
| Dernière modification le : Vendredi 10 Juillet 2009, 21:34:13 | |
