MATH-671 Analysis on Complex Manifolds 3 hours
Vector Bundles, Almost Complex Manifolds, the Cannonical Connection and Curvature of a Hermitian Holomorphic Vector Bundle, Sobolev Spaces, Differential Operators, Kaehler Manifold, Differential Operators on a Kaehler Manifold. The Hodge decompostion Theorem on compact Kaehler manifolds, Kodaira's vanishing theorem, Hodge manifolds.
1. Differential Analysis on Complex Manifolds, By Wells, Graduate Texts in Mathematics, Springer Verlag.
2. Foundations of Differentiable manifolds and Lie Groups, By Warner, Academic Press, New York.