Complex Geometry of Nature and General Relativity
by Giampiero Esposito
Publisher: arXiv 1999
Number of pages: 229
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.
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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 Daniele Angella, Cristiano Spotti - arXiv.org
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.
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 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.