Kähler-Einstein metrics: Old and New
by Daniele Angella, Cristiano Spotti
Publisher: arXiv.org 2017
Number of pages: 48
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 the SMI course 'Kaehler-Einstein metrics' given by C.S. in Cortona (Italy), May 2017.
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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 Gerald Kaiser - University of Massachusetts at Lowell
A new synthesis of the principles of quantum mechanics and Relativity is proposed in the context of complex differential geometry. The positivity of the energy implies that wave functions and fields can be extended to complex spacetime.
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.