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.Wells, R. O. is the author of 'Differential Analysis on Complex' with ISBN 9780387904191 and ISBN 0387904190.
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