  We investigate quaternionic contact (qc) manifolds from the point of view of
intrinsic torsion. We argue that the natural structure group for this geometry
is a non-compact Lie group K containing Sp(n)H^*, and show that any qc
structure gives rise to a canonical K-structure with constant intrinsic
torsion, except in seven dimensions, when this condition is equivalent to
integrability in the sense of Duchemin.
  We prove that the choice of a reduction to Sp(n)H^* (or equivalently, a
complement of the qc distribution) yields a unique K-connection satisfying
natural conditions on torsion and curvature.
  We show that the choice of a compatible metric on the qc distribution
determines a canonical reduction to Sp(n)Sp(1) and a canonical
Sp(n)Sp(1)-connection whose curvature is almost entirely determined by its
torsion. We show that its Ricci tensor, as well as the Ricci tensor of the
Biquard connection, has an interpretation in terms of intrinsic torsion.

Differential Geometry