Riemannian curvature: variations on different notions of positivity

Details Riemannian curvature: variations on different notions of positivity Riemannian curvature: variations on different notions of positivity

2006-11-13

arxiv.org/abs/math/0611371v1

Habilitation thesis, July 2006, Montpellier II University, France

Mathematics

Differential Geometry

In french, extracted from habilitation thesis at Montpellier II University (France), 50 pages

Scientific paper

We study different notions of Riemannian curvatures: The $p$-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 $(p,q)$-curvatures, which incorporate all the previous curvatures. We then examine the curvature term which appears in the classical Weitzenb\"ock formula. We also study the positivity properties of the $p$-curvatures, the second Gauss-Bonnet-Weyl curvature, the Einstein curvature and the isotropic curvature.

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