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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.


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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