Sufficient conditions for the extension ofC R structures
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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 PhrasesExtension ofC R structures integrable almost complex structures Kuranishi embedding problem
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