A Bonnet-Myers type theorem for quaternionic contact structures
Differential Geometry
2018-12-11 v3 Metric Geometry
Optimization and Control
Abstract
We prove a Bonnet-Myers type theorem for quaternionic contact manifolds of dimension bigger than 7. If the manifold is complete with respect to the natural sub-Riemannian distance and satisfies a natural Ricci-type bound expressed in terms of derivatives up to the third order of the fundamental tensors, then the manifold is compact and we give a sharp bound on its sub-Riemannian diameter.
Cite
@article{arxiv.1703.04340,
title = {A Bonnet-Myers type theorem for quaternionic contact structures},
author = {Davide Barilari and Stefan Ivanov},
journal= {arXiv preprint arXiv:1703.04340},
year = {2018}
}
Comments
21 pages, v2 minor corrections, v3 final draft version. To appear on Calc. Var. PDE