Complex Manifolds without Potential Theory: with an appendix on the geometry of characteristic classes

✍ Scribed by Dr. Shiing-shen Chern (auth.)

• Publisher: Springer-Verlag New York
• Year: 1979
• Tongue: English
• Leaves: 158
• Series: Universitext
• Edition: 2
• 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

Front Matter....Pages i-v
Introduction and Examples....Pages 1-6
Complex and Hermitian Structures on a Vector Space....Pages 6-12
Almost Complex Manifolds; Integrability Conditions....Pages 12-23
Sheaves and Cohomology....Pages 23-31
Complex Vector Bundles; Connections....Pages 31-46
Holomorphic Vector Bundles and Line Bundles....Pages 46-55
Hermitian Geometry and Kählerian Geometry....Pages 55-68
The Grassmann Manifold....Pages 68-83
Curves in a Grassmann Manifold....Pages 83-94
Back Matter....Pages 95-154

✦ Subjects

Analysis