Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds - Département de mathématiques appliquées Accéder directement au contenu
Article Dans Une Revue Journal of the Institute of Mathematics of Jussieu Année : 2019

Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds

Résumé

For a fat sub-Riemannian structure, we introduce three canonical Ricci curvatures in the sense of Agrachev-Zelenko-Li. Under appropriate bounds we prove comparison theorems for conjugate lengths, Bonnet-Myers type results and Laplacian comparison theorems for the intrinsic sub-Laplacian. As an application, we consider the sub-Riemannian structure of 3-Sasakian manifolds, for which we provide explicit curvature formulas. We prove that any complete 3-Sasakian structure of dimension 4d + 3, with d > 1, has sub-Riemannian diameter bounded by π. When d = 1, a similar statement holds under additional Ricci bounds. These results are sharp for the natural sub-Riemannian structure of the quaternionic Hopf fibrations on the 4d+3 dimensional sphere, whose exact sub-Riemannian diameter is π, for all d ≥ 1.
Fichier principal
Vignette du fichier
fat-comparison-v2.pdf (706.97 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01221661 , version 1 (28-10-2015)

Identifiants

Citer

Luca Rizzi, Pavel Silveira. Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds. Journal of the Institute of Mathematics of Jussieu, 2019, 18 (4), pp.783-827. ⟨10.1017/S1474748017000226⟩. ⟨hal-01221661⟩
443 Consultations
126 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More