Global minimality of generic manifolds and holomorphic extendibility of CR functions

Details Global minimality of generic manifolds and holomorphic extendibility of CR functions Global minimality of generic manifolds and holomorphic extendibility of CR functions

2004-11-26

arxiv.org/abs/math/0411592v1

Internat. Math. Res. Notices 1994, no. 8, 329 ff., approx. 14 pp. (electronic)

Mathematics

Complex Variables

13 pages, 0 figure

Scientific paper

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.

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