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Tenseur d'impulsion-énergie et géométrie spinorielle extrinsèque

Abstract : The results of this thesis are motivated by a better understanding of the energy-momentum tensor in spin geometry. We first investigate extrinsic spin geometry. We give relations between restrictions to a Riemannian submanifold of spinorial objects and objects defined in an intrinsinsic way. We then prove estimates for the first eigenvalue of a Dirac operator which is defined on compact spin Riemannian submanifolds. It turns out that the study of hypersurfaces gives a natural setup for the study of the energy-momentum tensor associated with a spinor field. We construct a generalized warped product which allows to consider this tensor as the second fundamental form of an isommetric immersion. Finally, we characterize surfaces in S^3 and H^3 in terms of special sections of the spin bundle, as well as parallel hypersurfaces in R^4.
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Contributor : Bertrand Morel Connect in order to contact the contributor
Submitted on : Thursday, January 29, 2004 - 3:55:00 PM
Last modification on : Friday, July 9, 2021 - 11:30:42 AM
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  • HAL Id : tel-01746714, version 2



Bertrand Morel. Tenseur d'impulsion-énergie et géométrie spinorielle extrinsèque. Mathématiques [math]. Université Henri Poincaré - Nancy 1, 2002. Français. ⟨NNT : 2002NAN10185⟩. ⟨tel-01746714v2⟩



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