East China Normal University
Group of Geometry
This is a lecture series about Complex Geometry. The lectures will talk about the following topics:
1. Basics of complex manifolds: Complex structure, examples, Cauchy-Riemann operator, Dolbeault complex, Dolbeaultcohomology
2. Metrics on complex manifolds: Hermitian manifolds, definitions of K?hler metrics, examples, Bergman metric, Laplace operator, Harmonic forms
3. Curvature: Hermitian vector bundles, connection, curvature operator, Ricci curvature, Chern classes, Bochner techniques and vanishing theorems
4. Hermitian symmetric spaces: Riemannian symmetric spaces,basics of Lie groups and lie algebras, Hermitian symmetric spaces, bounded symmetric domains
This is the first lecture. The talk will be given in Chinese. Everyone is welcome.