Complex manifolds without potential theory

✍ Scribed by Chern S.S.

• Publisher: Springer
• Year: 1995
• Tongue: English
• Leaves: 169
• Series: With an Appendix on the Geometry of Characteristic Classes
• Edition: 2ed
• Category: Library

✦ Synopsis

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#

✦ Table of Contents

Cover ......Page 1
Title ......Page 4
C) ......Page 5
Preface ......Page 6
Contents ......Page 7
1. Introduction and Examples ......Page 8
2. Complex and Hermitlan Structures on a Vector Space ......Page 13
3. Almost Complex Manifolds: Integrability Conditions ......Page 19
4. Sheaves and Cohomology ......Page 30
5. Complex Vector Bundles: Connections ......Page 38
6. Holomorphic Vector Bundles and Line Bundles ......Page 53
7. Hermitian Geometry and Kahlerian Geometry ......Page 62
8. The Grassmann Manifold ......Page 75
9. Curves in a Grassmann Manifold ......Page 90
Bibliography ......Page 102
1. Historical Remarks and Examples ......Page 104
2. Connections ......Page 113
3. Weil Homomorphism ......Page 120
4. Secondary Invariants ......Page 126
5. Vector Fields and Characteristic Numbers ......Page 138
6. Holomorphic Curves ......Page 147
7. Chern-Simons Invariant of Three-dimensional Manifolds ......Page 155
References ......Page 162
Index ......Page 166