Generalized Bochner formulas and Ricci lower bounds for sub-Riemannian manifolds of rank two
| dc.creator | Baudoin, Fabrice | |
| dc.creator | Garofalo, Nicola | |
| dc.date | 2009-04-10 | |
| dc.date.accessioned | 2026-07-07T13:02:23Z | |
| dc.date.available | 2026-07-07T13:02:23Z | |
| dc.description | We study a new class of rank two sub-Riemannian manifolds encompassing Riemannian manifolds, CR manifolds with vanishing Webster-Tanaka torsion, orthonormal bundles over Riemannian manifolds, and graded nilpotent Lie groups of step two. These manifolds admit a canonical horizontal connection and a canonical sub-Laplacian. We construct on these manifolds an analogue of the Riemannian Ricci tensor and prove Bochner type formulas for the sub-Laplacian. As a consequence, it is possible to formulate on these spaces a sub-Riemannian analogue of the so-called curvature dimension inequality. Sub-Riemannian manifolds for which this inequality is satisfied are shown to share many properties in common with Riemannian manifolds whose Ricci curvature is bounded from below | |
| dc.description | 71 pages | |
| dc.identifier | https://arxiv.org/abs/0904.1623 | |
| dc.identifier | http://arxiv.org/abs/0904.1623 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226433 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.title | Generalized Bochner formulas and Ricci lower bounds for sub-Riemannian manifolds of rank two | |
| dc.type | text |