Differential Analysis on Complex Manifolds

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 K??hler manifold, the Hodge decomposition theorem on compact K??hler manifolds, the Hodge-Riemann bilinear relations on K??hler manifolds Griffithsa??s period mapping, quadratic transformations, and Kodairaa??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.