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Habilitation à diriger des recherches

Courbure riemannienne: variations sur différentes notions de positivité

Abstract : We study different notions of Riemannian curvatures:
The $p$-curvatures interpolate between the scalar curvature and the sectional curvature, the
Gauss-Bonnet-Weyl curvatures form another interpolation from the scalar curvature to the Gauss-Bonnet integrand. We bring out the
$(p,q)$-curvatures, which incorporate all the previous curvatures. We then examine the curvature term which appears in the classical
Weitzenböck formula. We also study the positivity properties of the $p$-curvatures, the second Gauss-Bonnet-Weyl curvature, the Einstein curvature and the isotropic curvature.
Document type :
Habilitation à diriger des recherches
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https://tel.archives-ouvertes.fr/tel-00267987
Contributor : Mohammed Larbi Labbi <>
Submitted on : Sunday, March 30, 2008 - 3:40:45 PM
Last modification on : Thursday, January 11, 2018 - 6:12:22 AM
Long-term archiving on: : Friday, May 21, 2010 - 1:02:09 AM

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  • HAL Id : tel-00267987, version 1

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Mohammed Larbi Labbi. Courbure riemannienne: variations sur différentes notions de positivité. Mathématiques [math]. Université Montpellier II - Sciences et Techniques du Languedoc, 2006. ⟨tel-00267987⟩

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