Differential Analysis on Complex Manifolds

R. O. Wells Jr. (auth.)9780387904191, 0387904190

In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Subsequent chapters then develop such topics as Hermitian exterior algebra and the Hodge-operator, harmonic theory on compact manifolds, differential operators on a Kahler manifold, the Hodge decomposition theorem on compact Kahler manifolds, the Hodge-Riemann bilinear relations on Kahler manifolds Griffiths’s period mapping, quadratic transformations, and Kodaira’s vanishing and embedding theorems.The third edition of this standard reference contains a new appendix by Oscar Garcia-Prada which gives an overview of the developments in the field during the decades since the book appeared.

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Table of contents :
Front Matter….Pages i-x
Manifolds and Vector Bundles….Pages 1-35
Sheaf Theory….Pages 36-64
Differential Geometry….Pages 65-107
Elliptic Operator Theory….Pages 108-153
Compact Complex Manifolds….Pages 154-216
Kodaira’s Projective Embedding Theorem….Pages 217-240
Back Matter….Pages 241-262