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.
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.
@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, Volume 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
,Cited by Sources: