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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The Levi form and local complex foliations
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by Michael Freeman PDF
Proc. Amer. Math. Soc. 57 (1976), 369-370 Request permission

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 $M$.
References
  • G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, No. 75, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1972. MR 0461588
  • Michael Freeman, Local complex foliation of real submanifolds, Math. Ann. 209 (1974), 1–30. MR 346185, DOI 10.1007/BF01432883
  • Peter Kraut, Zu einem Satz von F. Sommer über eine komplexanalytische Blätterung reeller Hyperflächen im $C^{n}$, Math. Ann. 174 (1967), 305–310 (German). MR 220970, DOI 10.1007/BF01364277
  • Friedrich Sommer, Komplex-analytische Blätterung reeller Mannigfaltigkeiten im $C^{n}$, Math. Ann. 136 (1958), 111–133 (German). MR 101924, DOI 10.1007/BF01362293
  • R. O. Wells, Jr., Function theory on differentiable manifolds, Contributions to Analysis, Academic Press, New York, 1974, pp. 407-441.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • 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