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AuthorChern, Shiing-shen. author
TitleComplex Manifolds without Potential Theory [electronic resource] : with an appendix on the geometry of characteristic classes / by Shiing-shen Chern
ImprintNew York, NY : Springer New York : Imprint: Springer, 1979
Edition Second Edition
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Descript V, 154 p. online resource


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#


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 Kรคhlerian 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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