New examples of non-locally embeddable C R structures (with no non-constant C R distributions)

Jean-Pierre Rosay

Annales de l'institut Fourier (1989)

  • Volume: 39, Issue: 3, page 811-823
  • ISSN: 0373-0956

Abstract

top
We construct examples of non-locally embeddable C R 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.

How to cite

top

Rosay, Jean-Pierre. "New examples of non-locally embeddable $CR$ structures (with no non-constant $CR$ distributions)." Annales de l'institut Fourier 39.3 (1989): 811-823. <http://eudml.org/doc/74853>.

@article{Rosay1989,
abstract = {We construct examples of non-locally embeddable $CR$ 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.},
author = {Rosay, Jean-Pierre},
journal = {Annales de l'institut Fourier},
keywords = {non locally embeddable CR structures},
language = {eng},
number = {3},
pages = {811-823},
publisher = {Association des Annales de l'Institut Fourier},
title = {New examples of non-locally embeddable $CR$ structures (with no non-constant $CR$ distributions)},
url = {http://eudml.org/doc/74853},
volume = {39},
year = {1989},
}

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
PB - Association des Annales de l'Institut Fourier
VL - 39
IS - 3
SP - 811
EP - 823
AB - We construct examples of non-locally embeddable $CR$ 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.
LA - eng
KW - non locally embeddable CR structures
UR - http://eudml.org/doc/74853
ER -

References

top
  1. [1] T. AKAHORI, A new approach to the local embedding theorem for CR structures for n ≥ 4, Memoirs of the AMS no. 336, Providence, RI 1987. Zbl0628.32025
  2. [2] D. HILL, What is the notion of a complex manifold with boundary, Prospect in Algebraic Analysis [M. Saito 60th birthday vol.]. 
  3. [3] H. JACOBOWITZ, The canonical bundle and realizable CR hypersurfaces, Pacific J. Math., 127 (1987), 91-101. Zbl0583.32050MR88e:32027
  4. [4] H. JACOBOWITZ, F. TRÈVES, Nonrealizable CR structures, Inventions Math., 66 (1982), 321-249. Zbl0487.32015
  5. [5] M. KURANISHI, 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. Zbl0576.32033MR84h:32023a
  6. [6] G. LUPACCIOLUA theorem on holomorphic extension for CR functions, Pacific J. Math., 124 (1986), 177-191. Zbl0597.32014MR87k:32026
  7. [7] L. NIRENBERG, Lectures on linear partial differential equations, Conference Board of Math. Sc., Regional Conference Series in mathematics No. 17, AMS, 1973. Zbl0267.35001MR56 #9048
  8. [8] L. NIRENBERG, On a question of Hans Lewy, Russian Math. Surveys, 29, (1974), 251-262. Zbl0305.35017MR58 #11823
  9. [9] J.P. ROSAY, E.L. STOUT, Rado's theorem for CR functions, to appear in Proc. AMS. Zbl0674.32007
  10. [10] M.C. SHAW, Hypoellipticity of a system of complex vector fiels, Duke Math. J., 50 no. 3 (1983), 713-728. Zbl0542.35021MR85e:35028
  11. [11] F. TRÈVES, Approximation and representation of functions and distributions annhilated by a system of complex vector fields, Ecole polytechnique (1981). Zbl0515.58030
  12. [12] F. TRÈVES, Introduction to pseudodifferential and Fourier Integral operators, Plenum (1980). Zbl0453.47027
  13. [13] S. WEBSTER, On the proof of Kuranishi's embedding theorem, (preprint). Zbl0679.32020
  14. [14] D. CATLIN, A Newlander Nirenberg theorem for manifolds with boundary, Mich. Math. J., 35 (1988), 233-240. Zbl0679.53029MR89j:32026

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.