2004/11/26 by Joel Merker
Mathematics · #math.CV #msc:32C16
published as Internat. Math. Res. Notices 1994, no. 8, 329 ff., approx. 14 pp. (electronic) · 13 pages, 0 figure
arxiv created 2004/11/26 · arxiv updated 2009/12/01
Let M be a smooth generic submanifold of Cn. 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.