Riemannian curvature: variations on different notions of positivity
arXiv:math/0611371
Abstract
We study different notions of Riemannian curvatures: The -curvatures which 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 -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 -curvatures, the second Gauss-Bonnet-Weyl curvature, the Einstein curvature and the isotropic curvature.
In french, extracted from habilitation thesis at Montpellier II University (France), 50 pages