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Complex Manifolds without Potential Theory

with an appendix on the geometry of characteristic classes

  • Textbook
  • © 1979

Overview

Authors:
  1. Shiing-shen Chern

    1. Department of Mathematics, University of California, Berkeley, USA

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Part of the book series: Universitext (UTX)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-v
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  2. Introduction and Examples

    • Shiing-shen Chern
    Pages 1-6

  3. Complex and Hermitian Structures on a Vector Space

    • Shiing-shen Chern
    Pages 6-12

  4. Almost Complex Manifolds; Integrability Conditions

    • Shiing-shen Chern
    Pages 12-23

  5. Sheaves and Cohomology

    • Shiing-shen Chern
    Pages 23-31

  6. Complex Vector Bundles; Connections

    • Shiing-shen Chern
    Pages 31-46

  7. Holomorphic Vector Bundles and Line Bundles

    • Shiing-shen Chern
    Pages 46-55

  8. Hermitian Geometry and Kählerian Geometry

    • Shiing-shen Chern
    Pages 55-68

  9. The Grassmann Manifold

    • Shiing-shen Chern
    Pages 68-83

  10. Curves in a Grassmann Manifold

    • Shiing-shen Chern
    Pages 83-94

  11. Back Matter

    Pages 95-154
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Keywords

About this book

From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress....
The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#

Reviews

From the reviews of the second edition: "The new methods of complex manifold theory are very useful tools for investigations in algebraic geometry, complex function theory, differential operators and so on. The differential geometrical methods of this theory were developed essentially under the influence of Professor S.-S. Chern's works. The present book is a second edition... It can serve as an introduction to, and a survey of, this theory and is based on the author's lectures held at the University of California and at a summer seminar of the Canadian Mathematical Congress.... The text is illustrated by many examples... The book is warmly recommended to everyone interested in complex differential geometry." #Acta Scientiarum Mathematicarum, 41, 3-4#

Authors and Affiliations

  • Department of Mathematics, University of California, Berkeley, USA

    Shiing-shen Chern

Bibliographic Information

  • Book Title: Complex Manifolds without Potential Theory

  • Book Subtitle: with an appendix on the geometry of characteristic classes

  • Authors: Shiing-shen Chern

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4684-9344-3

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: S.-s. Chern 1979

  • Softcover ISBN: 978-0-387-90422-1Published: 18 June 1979

  • eBook ISBN: 978-1-4684-9344-3Published: 29 June 2013

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 2

  • Number of Pages: V, 154

  • Additional Information: Originally published by Van Nostrand, 1968

  • Topics: Analysis

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