復(fù)流形上的微分分析

內(nèi)容概要

this book is an outgrowth and a considerable expansion of lectures given at Brandeis University in 1967-1968 and at Rice University in 1968-1969. The first four chapters are an attempt to survey in detail some recent developments in four somewhat different areas, of mathematics: geometry (manifolds and vector bundles), algebraic topology, differential geometry, and partial differential equations. In these chapters, I have developed various tools that are useful in the study of compact complex manifolds. My motivation for the choice of topics developed was governed mainly by the applications anticipated in the last two chapters. Two principal topics developed include Hodge's theory of harmonic integrals and Kodaira's characterization of projective algebraic manifolds.

書籍目錄

Chapter I Manifolds and Vector Bundles   1. Manifolds   2. Vector Bundles   3. Almost Complex Manifolds and thecS-Operator Chapter II Sheaf Theory   1. Presheaves and Sheaves   2. Resolutions of Sheaves   3. Cohomology Theory Appendix A. Cech Cohomology with Coefficients in a Sheaf ChaptercHI Differential Geometry   1. Hermitian Differential Geometry   2. ThecCanonical Connectioncand Curvaturecofca Hermitian Holomorphic Vector Bundle   3. Chern Classescof Differentiable Vector Bundles   4. Complex Line Bundles Chapter IV Elliptic Operator Theory   1. Sobolev Spaces   2. Differential Operators   3. Pseudodifferential Operators   4. A Parametrixcfor Elliptic Differential Operators   5. Elliptic Complexes Chapter V Compact Complex Manifolds   1. Hermitian Exterior Algebraconca Hermitian Vector Space   2. Harmonic Theorycon Compact Manifolds   3. Representations of st(2,cC) on Hermitian Exterior Algebras   4. Differential Operatorsconca Kahier Manifold   5. The Hodge Decomposition Theoremcon Compact Kahler Manifolds   6. ThecHodge-Riemann Bilinear Relationsconca Kahler Manifoldc Chapter VI Kodaira's Projective Embedding Theorem   1. HodgeManifolds   2. Kodaira's Vanishing Theorem   3. Quadratic Transformations   4. Kodaira's Embedding Theorem References Subject Index Author Index

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