MAGIC044: Complex Differential Geometry

Course details


Autumn 2009
Monday, October 5th to Friday, December 11th


Live lecture hours
Recorded lecture hours
Total advised study hours


S. Kobayashi and K. Nomizu, "Foundations of Differential Geometry", vol. II, John Wiley & Sons
A. Moroianu, "Lectures on Kähler Geometry", CUP
C. Voisin, "Hodge theory and complex algebraic geometry", vol. I, CUP
P. Griffiths and J. Harris, "Principles of Algebraic Geometry", John Wiley & Sons (chapter 0 only)

Additional reading material
K. Fritzsche and H. Grauert, "From Holomorphic Functions to Complex Manifolds", Springer
D. Huybrechts, "Complex Geometry, Springer
W. Ballman, "Lectures on Kähler manifolds", EMS
R.O. Wells, "Differential analysis on complex manifolds", Springer


Familiarity with basic notions of topological and differentiable manifolds, especially tensors and differential forms.
Knowledge of such Riemannian concepts as the Levi-Civita connection and curvature will be helpful, but not essential.


1. Complex and almost complex manifolds
2. Holomorphic forms and vector fields
3. Complex and holomorphic vector bundles
4. Hermitian bundles, metric connections, curvature
5. Chern classes
6. Hermitian and Kähler metrics
7. Dolbeaut theory and the Hodge theorem
8. Curvature of Kähler manifolds; holomorphic sectional curvature
9. Ricci curvature of Kähler manifolds
10. Kähler-Einstein manifolds
11. Calabi-Yau manifolds


  • RB

    Prof Roger Bielawski

    University of Leeds


Follow the link for a book to take you to the relevant Google Book Search page

You may be able to preview the book there and see links to places where you can buy the book. There is also link marked 'Find this book in a library' - this sometimes works well, but not always - you will need to enter your location, but it will be saved after you do that for the first time.


Attention needed

Assessment information will be available nearer the time.


Only consortium members have access to these files.

Please log in to view course materials.


Please log in to view lecture recordings.