Lectures on Kahler Geometry

Informationen zum Autor Andrei Moroianu is a Researcher at CNRS and a Professor of Mathematics at Ecole Polytechnique. Klappentext Graduate text providing a concise and self-contained introduction to K hler geometry. Zusammenfassung Kähler geometry is of substantial interest to both mathematicians and physicists and this graduate text provides a self-contained introduction to the subject. Topics discussed include complex manifolds and holomorphic vector bundles; Kähler manifolds and Hodge and Dolbeault theories; compact Kähler manifolds and a proof of the famous Kähler identities. Inhaltsverzeichnis 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.

Product details

• Authors: Andrei Moroianu, Andrei (Ecole Polytechnique Moroianu
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 29.03.2007
• EAN: 9780521688970
• ISBN: 978-0-521-68897-0
• No. of pages: 182
• Series: London Mathematical Society Student Texts
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Geometry