Résumé
We study different notions of Riemannian curvatures: <br />The $p$-curvatures interpolate between the scalar curvature and the sectional curvature, the <br />Gauss-Bonnet-Weyl curvatures form another interpolation from the scalar curvature to the Gauss-Bonnet integrand. We bring out the <br />$(p,q)$-curvatures, which incorporate all the previous curvatures. We then examine the curvature term which appears in the classical <br />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.