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Proceedings of the American Mathematical Society

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

 
 

 

Real-analytic submanifolds of complex manifolds


Author: L. R. Hunt
Journal: Proc. Amer. Math. Soc. 29 (1971), 69-74
MSC: Primary 32.40
DOI: https://doi.org/10.1090/S0002-9939-1971-0274801-9
MathSciNet review: 0274801
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Abstract: This paper examines the extendibility of holomorphic functions on a real manifold which is embedded in a complex manifold. The principal result is that all real k-dimensional, real-analytic, compact manifolds embedded in an n-dimensional complex Stein manifold, where $ k > n$, are extendible over a manifold of one higher real dimension. A discussion is also given of the local equations of a manifold which is C-R in a neighborhood of some point.


References [Enhancements On Off] (What's this?)

  • [1] S. J. Greenfield, Cauchy-Riemann equations in several variables, Ann. Scuola Norm. Sup. Pisa (3) 22 (1968), 275-314. MR 38 #6097. MR 0237816 (38:6097)
  • [2] L. R. Hunt, Exceptional points of a differentiable submanifold of a complex manifold (to appear).
  • [3] R. O. Wells, Jr., Concerning the envelope of holomorphy of a compact differentiable submanifold of a complex manifold, Ann. Scuola Norm. Sup. Pisa (3) 23 (1969), 347-361. MR 39 #7141. MR 0245835 (39:7141)
  • [4] -, Holomorphic hulls and holomorphic convexity of differentiable submanifolds, Trans. Amer. Math. Soc. 132 (1968), 245-262. MR 36 #5392. MR 0222340 (36:5392)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0274801-9
Keywords: Extendibility of holomorphic functions, real-analytic submanifolds of complex manifolds, exceptional points, locally C-R
Article copyright: © Copyright 1971 American Mathematical Society

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