e-books in Complex Differential Geometry category
Kähler-Einstein metrics: Old and Newby Daniele Angella, Cristiano Spotti - arXiv.org , 2017
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.
(6051 views)
Complex Manifoldsby Julius Ross - Stanford University , 2014
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.
(5897 views)
Differential Geometry of Indefinite Complex Submanifolds in Indefinite Complex Space Formsby Alfonso Romero, Young Jin Suh , 2004
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.
(8230 views)
Lectures On Levi Convexity Of Complex Manifolds And Cohomology Vanishing Theoremsby E. Vesentini - Tata Institute Of Fundamental Research , 1967
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.
(9774 views)
Lectures on Complex Analytic Manifoldsby L. Schwartz - Tata Institute of Fundamental Research , 1955
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.
(11171 views)
Quantum Physics, Relativity, and Complex Spacetimeby Gerald Kaiser - University of Massachusetts at Lowell , 2003
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.
(14947 views)
Complex Manifolds and Hermitian Differential Geometryby Andrew D. Hwang - University of Toronto , 1997
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.
(12046 views)
Complex Geometry of Nature and General Relativityby Giampiero Esposito - arXiv , 1999
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.
(16966 views)
Dynamics in One Complex Variableby John Milnor - Princeton University Press , 1991
This text studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself, concentrating on the case of rational maps of the Riemann sphere. The book introduces some key ideas in the field, and forms a basis for further study.
(16273 views)
Complex Analytic and Differential Geometryby Jean-Pierre Demailly - Universite de Grenoble , 2007
Basic concepts of complex geometry, coherent sheaves and complex analytic spaces, positive currents and potential theory, sheaf cohomology and spectral sequences, Hermitian vector bundles, Hodge theory, positive vector bundles, etc.
(18687 views)