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Tenseur d'impulsion-énergie et feuilletages

Abstract : The main subject of this thesis is to understand the energy-momentum tensor in the case of foliations. We first investigate the transverse spin geometry. We define the basic Dirac operator on Riemannian foliations and we establish a Schrodinger-Lichnerowicz formula. We then give inequalities of Fridrch type and Kirchberg types in the case of Kahler foliations. The case of Riemannian flows allows us for a better understand of the energy-momentum tensor in the case of foliations. It turns out that a natural skew-symmetric tensor appears that can be identified with the O'Neill tensor of the flow. Finally, we characterize the 3-dimmensional case by a solution of the Dirac equation.
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Contributor : Georges Habib <>
Submitted on : Monday, November 27, 2006 - 5:56:32 PM
Last modification on : Friday, February 26, 2021 - 3:21:55 AM
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  • HAL Id : tel-01754367, version 2



Georges Habib. Tenseur d'impulsion-énergie et feuilletages. Mathématiques [math]. Université Henri Poincaré - Nancy 1, 2006. Français. ⟨NNT : 2006NAN10054⟩. ⟨tel-01754367v2⟩



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