## e-books in Complex Differential Geometry category

**Kähler-Einstein metrics: Old and New**

by

**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.

(

**760**views)

**Complex Manifolds**

by

**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.

(

**934**views)

**Differential Geometry of Indefinite Complex Submanifolds in Indefinite Complex Space Forms**

by

**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.

(

**3608**views)

**Lectures On Levi Convexity Of Complex Manifolds And Cohomology Vanishing Theorems**

by

**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.

(

**4461**views)

**Lectures on Complex Analytic Manifolds**

by

**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.

(

**6184**views)

**Quantum Physics, Relativity, and Complex Spacetime**

by

**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.

(

**9088**views)

**Complex Manifolds and Hermitian Differential Geometry**

by

**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.

(

**6563**views)

**Complex Geometry of Nature and General Relativity**

by

**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.

(

**10692**views)

**Dynamics in One Complex Variable**

by

**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.

(

**9299**views)

**Complex Analytic and Differential Geometry**

by

**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.

(

**11523**views)