A local Blaschke-Petkantschin formula in a Riemannian manifold
Résumé
In this paper, we show a local Blaschke-Petkantschin formula for a Riemannian manifold. Namely, we compute the Jacobian determinant of the parametrization of (n + 1)-tuples of the manifold by the center and the radius of their common circumscribed sphere as well as the (n + 1) directions characterizing the positions of the n + 1 points on it. We deduce from it a more explicit two-term expansion when the radius tends to 0. This formula contains a local correction with respect to the flat case which involves the Ricci curvatures in the (n + 1) directions.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
Loading...