The topology of quaternionic contact manifolds

Abstract

We explore the consequences of curvature and torsion on the topology of quaternionic contact manifolds with integrable vertical distribution establishing a general Myers theorem for quaternionic contact manifolds of positive horizontal Ricci curvature. We introduce the category of almost Einstein quaternionic manifolds, characterized by the vanishing of one component of the torsion for the Biquard connection. Under the assumption of non-positive horizontal sectional curvatures, we show that the universal cover of any complete almost Einstein quaternionic contact manifold is either $$\mathbb {R}^{h+3}$$ or $$\mathbb {R}^h \times \mathbb {S}^3$$ .