Embeddability of abstract CR structures and integrability of related systems
Annales de l'Institut Fourier, Tome 37 (1987) no. 3, p. 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},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {37},
     number = {3},
     year = {1987},
     pages = {131-141},
     doi = {10.5802/aif.1101},
     zbl = {0619.58001},
     mrnumber = {89c:32053},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/AIF_1987__37_3_131_0/

[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 87i:32028 | Zbl 0598.32019

[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 82f:35057 | Zbl 0491.35036

[3] L. Hörmander, The Frobenius-Nirenberg theorem, Arkiv För Mat., 5-29 (1964), 425-432. | Zbl 0136.09104

[4] H. Jacobowitz, The canonical bundle and realizable CR hypersurfaces, preprint. | Zbl 0583.32050

[5] H. Jacobowitz and F. Treves, Non-realizable CR structures, Invent. Math., 66 (1982), 231-149. | MR 83f:53022 | Zbl 0487.32015

[6] A. Newlander and L. Nirenberg, Complex coordinates in almost complex manifolds, Ann. of Math., (2) 65 (1957), 391-404. | MR 19,577a | Zbl 0079.16102

[7] L. Nirenberg, A Complex Frobenius Theorem, Seminar on analytic functions I, Princeton, (1957), 172-189. | Zbl 0099.37502

[8] L. Nirenberg, On a question of Hans Lewy, Russian Math. Surveys, 29 (1974), 251-262. | MR 58 #11823 | Zbl 0305.35017

[9] F. Treves, Approximation and Representation of Functions and Distributions Annihilated by a System of Complex Vector Fields, Ecole Polytechnique, Palaiseau, France, (1981). | MR 84k:58008 | Zbl 0515.58030