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Symplectic Manifolds With No Kaehler Structure


Symplectic Manifolds With No Kaehler Structure
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Symplectic Manifolds With No Kaehler Structure


Symplectic Manifolds With No Kaehler Structure
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Author : Alesky Tralle
language : en
Publisher: Springer
Release Date : 2006-11-14

Symplectic Manifolds With No Kaehler Structure written by Alesky Tralle and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.


This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. In recent years, some new and stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture, the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (e.g. Thurston's conjecture and Sullivan's problem). Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. We expect that the reader is aware of the basics of differential geometry and algebraic topology at graduate level.



Symplectic Manifolds With No K Hler Structure


Symplectic Manifolds With No K Hler Structure
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Author : Aleksy Tralle
language : en
Publisher:
Release Date : 1997

Symplectic Manifolds With No K Hler Structure written by Aleksy Tralle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Homotopy theory categories.




Lectures On Symplectic Geometry


Lectures On Symplectic Geometry
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Author : Ana Cannas da Silva
language : en
Publisher: Springer
Release Date : 2004-10-27

Lectures On Symplectic Geometry written by Ana Cannas da Silva and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-27 with Mathematics categories.


The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.



Symplectic Manifolds With No Kaehler Structure


Symplectic Manifolds With No Kaehler Structure
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Author : Alesky Tralle
language : en
Publisher:
Release Date : 2014-09-01

Symplectic Manifolds With No Kaehler Structure written by Alesky Tralle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.




Locally Conformal K Hler Geometry


Locally Conformal K Hler Geometry
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Author : Sorin Dragomir
language : en
Publisher: Springer Science & Business Media
Release Date : 1998

Locally Conformal K Hler Geometry written by Sorin Dragomir and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.


. E C, 0 1'1 1, and n E Z, n ~ 2. Let~.. be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.



Deformations Of Mathematical Structures


Deformations Of Mathematical Structures
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Author : Julian Lawrynowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Deformations Of Mathematical Structures written by Julian Lawrynowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


Selected Papers from the Seminar on Deformations, Lódz-Lublin, 1985/87



Fundamental Groups Of Compact Kahler Manifolds


Fundamental Groups Of Compact Kahler Manifolds
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Author : Jaume Amorós
language : en
Publisher: American Mathematical Soc.
Release Date : 1996

Fundamental Groups Of Compact Kahler Manifolds written by Jaume Amorós and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.


This book is an exposition of what is currently known about the fundamental groups of compact Kähler manifolds. This class of groups contains all finite groups and is strictly smaller than the class of all finitely presentable groups. For the first time ever, this book collects together all the results obtained in the last few years which aim to characterize those infinite groups which can arise as fundamental groups of compact Kähler manifolds. Most of these results are negative ones, saying which groups don not arise. The methods and techniques used form an attractive mix of topology, differential and algebraic geometry, and complex analysis. The book would be useful to researchers and graduate students interested in any of these areas, and it could be used as a textbook for an advanced graduate course. One of its outstanding features is a large number of concrete examples. The book contains a number of new results and examples which have not appeared elsewhere, as well as discussions of some important open questions in the field.



Fifth International Congress Of Chinese Mathematicians


Fifth International Congress Of Chinese Mathematicians
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Author : Lizhen Ji
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Fifth International Congress Of Chinese Mathematicians written by Lizhen Ji and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.


This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.



Lectures On K Hler Manifolds


Lectures On K Hler Manifolds
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Author : Werner Ballmann
language : en
Publisher: European Mathematical Society
Release Date : 2006

Lectures On K Hler Manifolds written by Werner Ballmann and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.


These notes are based on lectures the author gave at the University of Bonn and the Erwin Schrodinger Institute in Vienna. The aim is to give a thorough introduction to the theory of Kahler manifolds with special emphasis on the differential geometric side of Kahler geometry. The exposition starts with a short discussion of complex manifolds and holomorphic vector bundles and a detailed account of the basic differential geometric properties of Kahler manifolds. The more advanced topics are the cohomology of Kahler manifolds, Calabi conjecture, Gromov's Kahler hyperbolic spaces, and the Kodaira embedding theorem. Some familiarity with global analysis and partial differential equations is assumed, in particular in the part on the Calabi conjecture. There are appendices on Chern-Weil theory, symmetric spaces, and $L^2$-cohomology.



The Geometry Of Walker Manifolds


The Geometry Of Walker Manifolds
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Author : Peter Gilkey
language : en
Publisher: Springer Nature
Release Date : 2022-05-31

The Geometry Of Walker Manifolds written by Peter Gilkey and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-31 with Mathematics categories.


This book, which focuses on the study of curvature, is an introduction to various aspects of pseudo-Riemannian geometry. We shall use Walker manifolds (pseudo-Riemannian manifolds which admit a non-trivial parallel null plane field) to exemplify some of the main differences between the geometry of Riemannian manifolds and the geometry of pseudo-Riemannian manifolds and thereby illustrate phenomena in pseudo-Riemannian geometry that are quite different from those which occur in Riemannian geometry, i.e. for indefinite as opposed to positive definite metrics. Indefinite metrics are important in many diverse physical contexts: classical cosmological models (general relativity) and string theory to name but two. Walker manifolds appear naturally in numerous physical settings and provide examples of extremal mathematical situations as will be discussed presently. To describe the geometry of a pseudo-Riemannian manifold, one must first understand the curvature of the manifold. We shall analyze a wide variety of curvature properties and we shall derive both geometrical and topological results. Special attention will be paid to manifolds of dimension 3 as these are quite tractable. We then pass to the 4 dimensional setting as a gateway to higher dimensions. Since the book is aimed at a very general audience (and in particular to an advanced undergraduate or to a beginning graduate student), no more than a basic course in differential geometry is required in the way of background. To keep our treatment as self-contained as possible, we shall begin with two elementary chapters that provide an introduction to basic aspects of pseudo-Riemannian geometry before beginning on our study of Walker geometry. An extensive bibliography is provided for further reading. Math subject classifications : Primary: 53B20 -- (PACS: 02.40.Hw) Secondary: 32Q15, 51F25, 51P05, 53B30, 53C50, 53C80, 58A30, 83F05, 85A04 Table of Contents: Basic Algebraic Notions / Basic Geometrical Notions / Walker Structures / Three-Dimensional Lorentzian Walker Manifolds / Four-Dimensional Walker Manifolds / The Spectral Geometry of the Curvature Tensor / Hermitian Geometry / Special Walker Manifolds