The Journal of Geometric Analysis

, Volume 4, Issue 4, pp 467-538

First online:

Sufficient conditions for the extension ofC R structures

  • David CatlinAffiliated withDepartment of Mathematics, Purdue University

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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 structures integrable almost complex structures Kuranishi embedding problem