  A contact projective structure is a contact path geometry the paths of which
are among the geodesics of some affine connection. In the manner of T.Y. Thomas
there is associated to each contact projective structure an ambient affine
connection on a symplectic manifold with one-dimensional fibers over the
contact manifold and using this the local equivalence problem for contact
projective structures is solved by the construction of a canonical regular
Cartan connection. This Cartan connection is normal if and only if an invariant
contact torsion vanishes. Every contact projective structure determines
canonical paths transverse to the contact structure which fill out the contact
projective structure to give a full projective structure, and the vanishing of
the contact torsion implies the contact projective ambient connection agrees
with the Thomas ambient connection of the corresponding projective structure.
An analogue of the classical Beltrami theorem is proved for pseudo-hermitian
manifolds with transverse symmetry.

Differential Geometry