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We apply the theory of Weyl structures for parabolic geometries developed byA. Cap and J. Slovak in to compute, for a quaternionic contact (qc) structure,the Weyl connection associated to a choice of scale, i.e. to a choice ofCarnot-Carath\'eodory metric in the conformal class. The result of thiscomputation has applications to the study of the conformal Fefferman space of aqc manifold. In addition to this application, we are also able to easilycompute a tensorial formula for the qc analog of the Weyl curvature tensor inconformal geometry and the Chern-Moser tensor in CR geometry. This tensoragrees with the formula derived via independent methods by S. Ivanov and D.Vasillev. However, as a result of our derivation of this tensor, itsfundamental properties -- conformal covariance, and that its vanishing is asharp obstruction to local flatness of the qc structure -- follow as easycorollaries from the general parabolic theory.

Weyl connections and the local sphere theorem for quaternionic contact structures