De nouveaux exemples de structures non réalisables sont donnés. Ils sont basés sur une construction simple qui consiste à recoller deux structures plongées. Ces exemples semblent améliorer en partie des exemples anciens de Nirenberg, et Jacobowitz et Trèves, mais l’avantage principal en est peut-être le caractère transparent, qui en rend l’étude facile.
We construct examples of non-locally embeddable structures. These examples may show some improvement on previous examples by Nirenberg, and Jacobowitz and Trèves. They are based on a simple construction which consists in gluing two embedded structures. And (this is our main point) we believe that these examples are very transparent, therefore easy to work with.
@article{AIF_1989__39_3_811_0, author = {Rosay, Jean-Pierre}, title = {New examples of non-locally embeddable $CR$ structures (with no non-constant $CR$ distributions)}, journal = {Annales de l'Institut Fourier}, pages = {811--823}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {39}, number = {3}, year = {1989}, doi = {10.5802/aif.1189}, mrnumber = {1030851}, zbl = {0674.32008}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1189/} }
TY - JOUR AU - Rosay, Jean-Pierre TI - New examples of non-locally embeddable $CR$ structures (with no non-constant $CR$ distributions) JO - Annales de l'Institut Fourier PY - 1989 SP - 811 EP - 823 VL - 39 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1189/ DO - 10.5802/aif.1189 LA - en ID - AIF_1989__39_3_811_0 ER -
%0 Journal Article %A Rosay, Jean-Pierre %T New examples of non-locally embeddable $CR$ structures (with no non-constant $CR$ distributions) %J Annales de l'Institut Fourier %D 1989 %P 811-823 %V 39 %N 3 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1189/ %R 10.5802/aif.1189 %G en %F AIF_1989__39_3_811_0
Rosay, Jean-Pierre. New examples of non-locally embeddable $CR$ structures (with no non-constant $CR$ distributions). Annales de l'Institut Fourier, Tome 39 (1989) no. 3, pp. 811-823. doi : 10.5802/aif.1189. https://aif.centre-mersenne.org/articles/10.5802/aif.1189/
[1] A new approach to the local embedding theorem for CR structures for n ≥ 4, Memoirs of the AMS no. 336, Providence, RI 1987. | Zbl
,[2] What is the notion of a complex manifold with boundary, Prospect in Algebraic Analysis [M. Saito 60th birthday vol.].
,[3] The canonical bundle and realizable CR hypersurfaces, Pacific J. Math., 127 (1987), 91-101. | MR | Zbl
,[4] Nonrealizable CR structures, Inventions Math., 66 (1982), 321-249. | Zbl
, ,[5] Strongly pseudoconvex CR structures over small balls, Ann. of Math., I 115 (1982), 451-500, II 116 (1982), 1-64, III 116 (1982), 249-330. | MR | Zbl
,[6] A theorem on holomorphic extension for CR functions, Pacific J. Math., 124 (1986), 177-191. | MR | Zbl
[7] Lectures on linear partial differential equations, Conference Board of Math. Sc., Regional Conference Series in mathematics No. 17, AMS, 1973. | MR | Zbl
,[8] On a question of Hans Lewy, Russian Math. Surveys, 29, (1974), 251-262. | MR | Zbl
,[9] Rado's theorem for CR functions, to appear in Proc. AMS. | Zbl
, ,[10] Hypoellipticity of a system of complex vector fiels, Duke Math. J., 50 no. 3 (1983), 713-728. | MR | Zbl
,[11] Approximation and representation of functions and distributions annhilated by a system of complex vector fields, Ecole polytechnique (1981). | Zbl
,[12] Introduction to pseudodifferential and Fourier Integral operators, Plenum (1980). | Zbl
,[13] On the proof of Kuranishi's embedding theorem, (preprint). | Numdam | Zbl
,[14] A Newlander Nirenberg theorem for manifolds with boundary, Mich. Math. J., 35 (1988), 233-240. | MR | Zbl
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