The Journal of Geometric Analysis

, Volume 4, Issue 4, pp 467–538

Sufficient conditions for the extension ofC R structures

  • David Catlin

DOI: 10.1007/BF02922141

Cite this article as:
Catlin, D. J Geom Anal (1994) 4: 467. doi:10.1007/BF02922141


LetM be a smoothC R manifold of dimension 2n − 1 such that at each point, either the Levi form has at least 3 positive eigenvalues or it hasn − 1 negative eigenvalues. IfD is a smoothly bounded subdomain ofM, then there is a smoothly bounded integrable almost complex manifoldX of dimension 2n such thatM is contained in the boundary ofX and such that theC R structure thatM inherits as a subset ofX coincides with the original structure ofM.

Math Subject Classification

(1985 Revision) 32G05

Key Words and Phrases

Extension ofC R structuresintegrable almost complex structuresKuranishi embedding problem

Copyright information

© Mathematica Josephina, Inc. 1994

Authors and Affiliations

  • David Catlin
    • 1
  1. 1.Department of MathematicsPurdue UniversityWest Lafayette