Differential analysis on complex manifolds

In developing 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-Riemann bilinear relations on Kähler manifolds Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems.