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The Levi form and local complex foliations


Author: Michael Freeman
Journal: Proc. Amer. Math. Soc. 57 (1976), 369-370
MSC: Primary 32F99
DOI: https://doi.org/10.1090/S0002-9939-1976-0409899-2
MathSciNet review: 0409899
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Abstract: A short coordinate-free proof is given for some known results on the existence of local complex-analytic foliations of a real submanifold $ M$ of $ {{\mathbf{C}}^n}$. The proof uses an explicit formulation of the equivalence between two definitions of the E. E. Levi form of $ M$.


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  • [3] P. Kraut, Zu einem Satz von F. Sommer über eine komplex-analytische Blätterung reeller Hyperflächen im $ {{\mathbf{C}}^n}$, Math. Ann. 174 (1967), 305-310. MR 36 #4022. MR 0220970 (36:4022)
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  • [5] R. O. Wells, Jr., Function theory on differentiable manifolds, Contributions to Analysis, Academic Press, New York, 1974, pp. 407-441.

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DOI: https://doi.org/10.1090/S0002-9939-1976-0409899-2
Keywords: Levi form, complex tangent, local complex foliation
Article copyright: © Copyright 1976 American Mathematical Society

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