  We show how the double vector bundle structure of the manifold of double
velocities, with its submanifolds of holonomic and semiholonomic double
velocities, is mirrored by a structure of holonomic and semiholonomic subgroups
in the principal prolongation of the first jet group. We use the actions of
these groups to construct holonomic and semiholonomic submanifolds in the
manifold of double contact elements, and show that these give rise to affine
bundles where a semiholonomic element has well-defined holonomic and curvature
components.
