A Bonnet-Myers type theorem for quaternionic contact structures

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.

21 pages, v2 minor corrections, v3 final draft version. To appear on Calc. Var. PDE