Complex Manifolds and Hermitian Differential Geometry
by Andrew D. Hwang
Publisher: University of Toronto 1997
Number of pages: 113
The intent of this text 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. The author provides a number of interesting and non-trivial examples, both in the text and in the exercises.
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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 L. Schwartz - Tata Institute of Fundamental Research
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; etc.
by E. Vesentini - Tata Institute Of Fundamental Research
These are notes of lectures which the author gave in the winter 1965. Topics covered: Vanishing theorems for hermitian manifolds; W-ellipticity on Riemannian manifolds; Local expressions for and the main inequality; Vanishing Theorems.
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We present classical and recent results on Kaehler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for author's course.