A twosided H. Lewy extension phenomenon
Authors:
L. R. Hunt and M. Kazlow
Journal:
Proc. Amer. Math. Soc. 74 (1979), 95100
MSC:
Primary 32D10
MathSciNet review:
521879
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Abstract: Let M be a real dimensional CRmanifold in . We are interested in finding conditions on M near a point which imply that all CRfunction on M extend to holomorphic functions in some fixed neighborhood of p in . Of course if M is a real hypersurface, it is known that M having eigenvalues of opposite sign in its Levi form at p will give us such an extension result. If we view the Levi form at a point on a general CRmanifold M as a quadratic map from the holomorphic tangent space to the normal space of the real tangent space in , and if this map is surjective, then we prove our CRfunctions extend to holomorphic functions in an open neighborhood of the point. We also show that if the real codimension of M in is 2, and if the Levi form is totally indefinite, then the Levi form is onto as a quadratic map, and hence we have our extension theory.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197905218798
PII:
S 00029939(1979)05218798
Keywords:
CRfunctions,
Levi form,
quadratic maps,
totally indefinite,
CRextension
Article copyright:
© Copyright 1979
American Mathematical Society
