Complex Differential Geometry

e-books in Complex Differential Geometry category

Book cover: Kähler-Einstein metrics: Old and NewKähler-Einstein metrics: Old and New
by - 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.
Book cover: Complex ManifoldsComplex Manifolds
by - 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.

Book cover: Lectures on Complex Analytic ManifoldsLectures on Complex Analytic Manifolds
by - 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.
Book cover: Quantum Physics, Relativity, and Complex SpacetimeQuantum Physics, Relativity, and Complex Spacetime
by - 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.
Book cover: Complex Manifolds and Hermitian Differential GeometryComplex Manifolds and Hermitian Differential Geometry
by - 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.
Book cover: Complex Geometry of Nature and General RelativityComplex Geometry of Nature and General Relativity
by - 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.
Book cover: Dynamics in One Complex VariableDynamics in One Complex Variable
by - Princeton University Press ,
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.
Book cover: Complex Analytic and Differential GeometryComplex Analytic and Differential Geometry
by - Universite de Grenoble ,
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.