Lectures on Complex Analytic Manifolds
by L. Schwartz
Publisher: Tata Institute of Fundamental Research 1955
Number of pages: 163
Topics covered: Differentiable Manifolds; C maps, diffeomorphisms. Effect of a map; The Tensor Bundles; Existence and uniqueness of the exterior differentiation; Manifolds with boundary; Integration on chains; Some examples of currents; Currents with compact support; de Rham's Theorem; The star operator; Green's Operator G; Real vector spaces with a J-Structure; The operator J; The canonical orientation of a complex manifold; etc.
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by Julius Ross - Stanford University
From the table of contents: Complex Manifolds; Almost Complex Structures; Differential Forms; Poincare Lemma; Sheaves and Cohomology; Several Complex Variables; Holomorphic Vector Bundles; Kaehler Manifolds; Hodge Theory; Lefschetz Theorems; etc.
by Alfonso Romero, Young Jin Suh
From the table of contents: Chapter 1. Linear preliminaries; Chapter 2. Indefinite Kaehler manifolds; Chapter 3. Complex hypersurfaces; Chapter 4. Complex submanifolds; Chapter 5. Totally real bisectional curvature; and more.
by Giampiero Esposito - arXiv
An attempt is made of giving a self-contained introduction to holomorphic ideas in general relativity, following work over the last thirty years by several authors. The main topics are complex manifolds, spinor and twistor methods, heaven spaces.
by Andrew D. Hwang - University of Toronto
The intent is not to give a thorough treatment of the algebraic and differential geometry of complex manifolds, but to introduce the reader to material of current interest as quickly as possible. A number of interesting examples is provided.