Differential Analysis on Complex Manifolds

  • Raymond O. WellsJr.

Part of the Graduate Texts in Mathematics book series (GTM, volume 65)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Raymond O. Wells Jr.
    Pages 1-35
  3. Raymond O. Wells Jr.
    Pages 36-64
  4. Raymond O. Wells Jr.
    Pages 65-107
  5. Raymond O. Wells Jr.
    Pages 108-153
  6. Raymond O. Wells Jr.
    Pages 154-216
  7. Raymond O. Wells Jr.
    Pages 217-240
  8. Back Matter
    Pages 241-302

About this book


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 certain developments in the field during the decades since the book first appeared.

From reviews of the 2nd Edition:

"..the new edition of Professor Wells' book is timely and excellent introduction for any mathematician who suspects that complex manifold techniques may be relevant to his work."

- Nigel Hitchin, Bulletin of the London Mathematical Society

"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."

- Daniel M. Burns, Jr., Mathematical Reviews


Analysis Differenzierbare Mannigfaltigkeit Komplexe Mannigfaltigkeit calculus differential equation differential geometry manifold operator theory partial differential equation

Authors and affiliations

  • Raymond O. WellsJr.
    • 1
  1. 1.Jacobs University BremenBremenGermany

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