Andrei Moroianu

Lectures on Kahler Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

Kahler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kahler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kahler identities. The final part of the text studies several aspects of compact Kahler manifolds: the Calabi conjecture, Weitzenbock techniques, Calabi-Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 29. März 2007
• Englisch
• ISBN-13: 9780511271694
• Artikelnr.: 38193399

Autorenporträt

Andrei Moroianu is a Researcher at CNRS and a Professor of Mathematics at Ecole Polytechnique.

Inhaltsangabe

Introduction
Part I. Basics on Differential Geometry: 1. Smooth manifolds
2. Tensor fields on smooth manifolds
3. The exterior derivative
4. Principal and vector bundles
5. Connections
6. Riemannian manifolds
Part II. Complex and Hermitian Geometry: 7. Complex structures and holomorphic maps
8. Holomorphic forms and vector fields
9. Complex and holomorphic vector bundles
10. Hermitian bundles
11. Hermitian and Kähler metrics
12. The curvature tensor of Kähler manifolds
13. Examples of Kähler metrics
14. Natural operators on Riemannian and Kähler manifolds
15. Hodge and Dolbeault theory
Part III. Topics on Compact Kähler Manifolds: 16. Chern classes
17. The Ricci form of Kähler manifolds
18. The Calabi-Yau theorem
19. Kähler-Einstein metrics
20. Weitzenböck techniques
21. The Hirzebruch-Riemann-Roch formula
22. Further vanishing results
23. Ricci-flat Kähler metrics
24. Explicit examples of Calabi-Yau manifolds
Bibliography
Index.