  Let M be a smooth generic submanifold of C^n. Tumanov showed that the
direction of CR extendability parallel propagates with respect to a certain
differential geometric partial connection in a quotient bundle of the normal
bundle to M. M is said to be globally minimal at a point z in M if the CR orbit
of z contains a neighborhood of z in M. It is shown that the vector space
generated by the directions of CR-extendability of CR functions on M is
preserved by the induced composed flow between two points in the same CR orbit.
As an application, the main result of this paper, conjectured by J.-M. Trepreau
in 1990, is established: for wedge extendability of CR functions to hold at
every point in the CR-orbit of z M, it is sufficient that M be globally minimal
at z.
