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Pré-Publication, Document De Travail Année : 1993

Global minimality of generic manifolds and holomorphic extendibility of CR functions

Résumé

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.
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Dates et versions

hal-00003369 , version 1 (27-11-2004)

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  • HAL Id : hal-00003369 , version 1

Citer

Joel Merker. Global minimality of generic manifolds and holomorphic extendibility of CR functions. 1993. ⟨hal-00003369⟩
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