H-type foliations
arXiv:1812.02563 · doi:10.1016/j.difgeo.2022.101952
Abstract
With a view toward sub-Riemannian geometry, we introduce and study H-type foliations. These structures are natural generalizations of K-contact geometries which encompass as special cases K-contact manifolds, twistor spaces, 3K contact manifolds and H-type groups. Under an horizontal Ricci curvature lower bound, we prove on those structures sub-Riemannian diameter upper bounds and first eigenvalue estimates for the sub-Laplacian. Then, using a result by Moroianu-Semmelmann, we classify the H-type foliations that carry a parallel horizontal Clifford structure. Finally, we prove an horizontal Einstein property and compute the horizontal Ricci curvature of those spaces in codimension more than 2.
arXiv commentaccepted version
References in corpus (6)
- A formula for Popp's volume in sub-Riemannian geometry
- Sub-Riemannian curvature in contact geometry
- Sharp measure contraction property for generalized H-type Carnot groups
- Clifford structures on Riemannian manifolds
- Sub-Riemannian Ricci curvatures and universal diameter bounds for 3-Sasakian manifolds
- A sub-Riemannian Santaló formula with applications to isoperimetric inequalities and first Dirichlet eigenvalue of hypoelliptic operators