Complex Manifolds without Potential Theory

1. Front Matter

   Pages i-v

   PDF

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

    PDF

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#

• Manifolds
• Potential theory
• Vector field
• differential geometry
• komplexe Mannigfaltigkeit
• manifold

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#

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

  Shiing-shen Chern

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