  We study the behavior of connections and curvature under the HK/QK
correspondence, proving simple formulae expressing the Levi-Civita connection
and Riemann curvature tensor on the quaternionic K\"ahler side in terms of the
initial hyper-K\"ahler data. Our curvature formula refines a well-known
decomposition theorem due to Alekseevsky. As an application, we compute the
norm of the curvature tensor for a series of complete quaternionic K\"ahler
manifolds arising from flat hyper-K\"ahler manifolds. We use this to deduce
that these manifolds are of cohomogeneity one.
