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Differential Analysis on Complex Manifolds
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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 Kähler manifold, the Hodge decomposition theorem on compact Kähler manifolds, the Hodge-Riemann bilinear relations on Kähler 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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