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 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 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 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.
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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.