Complex manifolds without potential theory : with an appendix on the geometry of characteristic classes

Shiing-Shen Chern

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#

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[目次]

  • 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 Kahlerian 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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この本の情報

書名 Complex manifolds without potential theory : with an appendix on the geometry of characteristic classes
著作者等 Chern, Shiing-Shen
シリーズ名 Universitext
出版元 Springer-Verlag
刊行年月 c1979
版表示 2nd ed
ページ数 152 p.
大きさ 24 cm
ISBN 3540904220
0387904220
NCID BA03507647
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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