Real-analytic submanifolds of complex manifolds
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- by L. R. Hunt PDF
- Proc. Amer. Math. Soc. 29 (1971), 69-74 Request permission
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
- S. J. Greenfield, Cauchy-Riemann equations in several variables, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 22 (1968), 275–314. MR 237816 L. R. Hunt, Exceptional points of a differentiable submanifold of a complex manifold (to appear).
- R. O. Wells Jr., Concerning the envelope of holomorphy of a compact differentiable submanifold of a complex manifold, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 23 (1969), 347–361. MR 245835
- R. O. Wells Jr., Holomorphic hulls and holomorphic convexity of differentiable submanifolds, Trans. Amer. Math. Soc. 132 (1968), 245–262. MR 222340, DOI 10.1090/S0002-9947-1968-0222340-8
Additional Information
- © Copyright 1971 American Mathematical Society
- 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