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Noncompact Complex Manifolds

In: Differential and Complex Geometry: Origins, Abstractions and Embeddings

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  • Raymond O. Wells Jr.

    (University of Colorado Boulder
    Jacobs University Bremen)

Abstract

Shortly after the work of Kodaira, various mathematicians were able to use some of the same tools to provide a characterization of which noncompact complex manifolds (now called Stein manifolds) could be embedded as closed complex submanifolds of a complex Euclidean space. In 1958, Grauert was able to use the Stein manifold embedding theorem to show that any real-analytic manifold can be real-analytically embedded in a real Euclidean space, a problem that had been proposed in the original paper of Whitney from 1936.

Suggested Citation

  • Raymond O. Wells Jr., 2017. "Noncompact Complex Manifolds," Springer Books, in: Differential and Complex Geometry: Origins, Abstractions and Embeddings, chapter 0, pages 269-302, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-58184-2_15
    DOI: 10.1007/978-3-319-58184-2_15
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