Embeddability of abstract CR structures and integrability of related systems
Annales de l'Institut Fourier, Tome 37 (1987) no. 3, pp. 131-141.

Des conditions nécessaires et suffisantes pour le plongement local de structures CR abstraites sont exprimées en terme de commutation des champs de vecteurs CR avec une algèbre de Lie complexe. Ces résultats s’étendent à des systèmes plus généraux.

Necessary and sufficient conditions for local embeddability of abstract CR structures are expressed in terms of the commutation of the CR vector fields with a complex Lie algebra. These results extend to more general systems.

@article{AIF_1987__37_3_131_0,
     author = {Baouendi, Salah and Rothschild, Linda P.},
     title = {Embeddability of abstract {CR} structures and integrability of related systems},
     journal = {Annales de l'Institut Fourier},
     pages = {131--141},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {37},
     number = {3},
     year = {1987},
     doi = {10.5802/aif.1101},
     mrnumber = {89c:32053},
     zbl = {0619.58001},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.1101/}
}
TY  - JOUR
AU  - Baouendi, Salah
AU  - Rothschild, Linda P.
TI  - Embeddability of abstract CR structures and integrability of related systems
JO  - Annales de l'Institut Fourier
PY  - 1987
SP  - 131
EP  - 141
VL  - 37
IS  - 3
PB  - Imprimerie Louis-Jean
PP  - Gap
UR  - https://www.numdam.org/articles/10.5802/aif.1101/
DO  - 10.5802/aif.1101
LA  - en
ID  - AIF_1987__37_3_131_0
ER  - 
%0 Journal Article
%A Baouendi, Salah
%A Rothschild, Linda P.
%T Embeddability of abstract CR structures and integrability of related systems
%J Annales de l'Institut Fourier
%D 1987
%P 131-141
%V 37
%N 3
%I Imprimerie Louis-Jean
%C Gap
%U https://www.numdam.org/articles/10.5802/aif.1101/
%R 10.5802/aif.1101
%G en
%F AIF_1987__37_3_131_0
Baouendi, Salah; Rothschild, Linda P. Embeddability of abstract CR structures and integrability of related systems. Annales de l'Institut Fourier, Tome 37 (1987) no. 3, pp. 131-141. doi : 10.5802/aif.1101. https://www.numdam.org/articles/10.5802/aif.1101/

[1] M. S. Baouendi, L. P. Rothschild and F. Treves, CR structures with group action and extendability of CR functions, Invent. Math., 83 (1985), 359-396. | MR | Zbl

[2] M. S. Baouendi and F. Treves, A property of the functions and distributions annihilated by a locally integrable system of complex vector fields, Ann. of Math., 113 (1981), 387-421. | MR | Zbl

[3] L. Hörmander, The Frobenius-Nirenberg theorem, Arkiv För Mat., 5-29 (1964), 425-432. | Zbl

[4] H. Jacobowitz, The canonical bundle and realizable CR hypersurfaces, preprint. | Zbl

[5] H. Jacobowitz and F. Treves, Non-realizable CR structures, Invent. Math., 66 (1982), 231-149. | MR | Zbl

[6] A. Newlander and L. Nirenberg, Complex coordinates in almost complex manifolds, Ann. of Math., (2) 65 (1957), 391-404. | MR | Zbl

[7] L. Nirenberg, A Complex Frobenius Theorem, Seminar on analytic functions I, Princeton, (1957), 172-189. | Zbl

[8] L. Nirenberg, On a question of Hans Lewy, Russian Math. Surveys, 29 (1974), 251-262. | MR | Zbl

[9] F. Treves, Approximation and Representation of Functions and Distributions Annihilated by a System of Complex Vector Fields, Ecole Polytechnique, Palaiseau, France, (1981). | MR | Zbl

Cité par Sources :