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Mathematics - Analysis | Complex Manifolds without Potential Theory - with an appendix on the geometry of characteristic

Complex Manifolds without Potential Theory

with an appendix on the geometry of characteristic classes

Series: Universitext

Chern, Shiing-shen

Originally published by Van Nostrand, 1968

2nd ed. 1979, V, 154 p.

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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#

Content Level » Graduate

Keywords » Manifolds - Potential theory - Vector field - differential geometry - komplexe Mannigfaltigkeit - manifold

Related subjects » Analysis

Table of contents 

1. Introduction and Examples.- 2. Complex and Hermitian Structures on a Vector Space.- 3. Almost Complex Manifolds; Integrability Conditions.- 4. Sheaves and Cohomology.- 5. Complex Vector Bundles; Connections.- 6. Holomorphic Vector Bundles and Line Bundles.- 7. Hermitian Geometry and Kählerian Geometry.- 8. The Grassmann Manifold.- 9. Curves in a Grassmann Manifold.- Appendix: Geometry of Characteristic Classes.- 1. Historical Remarks and Examples.- 2. Weil Homomorphism.- 3. Secondary Invariants.- 5. Vector Fields and Characteristic Numbers.- 6. Holomorphic Curves.- References.

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