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. Trépreau in 1990, is established: for wedge extendability of CR functions to hold at every point in the CR-orbit of z in M, it is sufficient that M be globally minimal at z.
Publié le : 1993-07-05
Classification:
CR functions,
Global minimality in the sense of Trepreau-Tumanov,
propagation of holomorphic extendability,
Generic submanifolds of C^n,
wedges,
CR-extension,
32C16 (32F25),
[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG],
[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]
@article{hal-00003369,
author = {Merker, Joel},
title = {Global minimality of generic manifolds and holomorphic extendibility of CR functions},
journal = {HAL},
volume = {1993},
number = {0},
year = {1993},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00003369}
}
Merker, Joel. Global minimality of generic manifolds and holomorphic extendibility of CR functions. HAL, Tome 1993 (1993) no. 0, . http://gdmltest.u-ga.fr/item/hal-00003369/