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An Introduction to Analysis on Complex Manifolds

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Part of the Lecture Notes in Mathematics book series (LNM,volume 950)

Abstract

We give an account of some of the analysis on complex manifolds leading in particular to Dolbeault cohomology and the Hodge decomposition Theorem. On the way we introduce some basic notions such as sheaves, connections in fibre bundles and Kähler manifolds. We thank Frl. A. Thiedemann for the difficult job of typing our illegible manuscript.

  1. 1

    Elementary Several Complex Variables.

  2. 2

    Analysis on Manifolds.

  3. 3

    Sheaves and Cohomology.

  4. 4

    Connections in Vector Bundles and Kähler Manifolds.

  5. 5

    Harmonic Theory on Compact Complex Manifolds.

  6. 6

    Cohomology of Kähler Manifolds.

Keywords

  • Vector Bundle
  • Holomorphic Function
  • Complex Manifold
  • Cohomology Group
  • Cohomology Class

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© 1982 Springer-Verlag Berlin Heidelberg

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Lemaire, L., Wood, J.C. (1982). An Introduction to Analysis on Complex Manifolds. In: Complex Analysis. Lecture Notes in Mathematics, vol 950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061876

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  • DOI: https://doi.org/10.1007/BFb0061876

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11596-0

  • Online ISBN: 978-3-540-39366-5

  • eBook Packages: Springer Book Archive