Lectures on Kahler Geometry (Hardcover)

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 Kahler metrics; 12. The curvature tensor of Kahler manifolds; 13. Examples of Kahler metrics; 14. Natural operators on Riemannian and Kahler manifolds; 15. Hodge and Dolbeault theory; Part III. Topics on Compact Kahler Manifolds: 16. Chern classes; 17. The Ricci form of Kahler manifolds; 18. The Calabi?Yau theorem; 19. Kahler?Einstein metrics; 20. Weitzenbock techniques; 21. The Hirzebruch?Riemann?Roch formula; 22. Further vanishing results; 23. Ricci?flat Kahler metrics; 24. Explicit examples of Calabi?Yau manifolds; Bibliography; Index.