Differential Analysis on Complex Manifolds

  • Springer
  • 2016
  • Elektronisk medie
  • 0
  • English
  • 3
  • 9780387738925

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.From a review of the 2nd Edition:&quote;..the new edition of Professor Wells' book is timely and welcome...an excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work.&quote;- Nigel Hitchin, Bulletin of the London Mathematical Society&quote;Its purpose is to present the basics of analysis and geometry on compact complex manifolds, and is already one of the standard sources for this material.&quote;