Download or read book Fundamental Groups of Compact Kahler Manifolds written by Jaume Amorós and published by American Mathematical Soc.. This book was released on 1996 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Lectures on K hler Manifolds written by Werner Ballmann and published by European Mathematical Society. This book was released on 2006 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Nonlinear Methods in Riemannian and K hlerian Geometry written by J. Jost and published by Birkhäuser. This book was released on 2013-04-17 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, I present an expanded version of the contents of my lectures at a Seminar of the DMV (Deutsche Mathematiker Vereinigung) in Diisseldorf, June, 1986. The title "Nonlinear methods in complex geometry" already indicates a combination of techniques from nonlinear partial differential equations and geometric concepts. In older geometric investigations, usually the local aspects attracted more attention than the global ones as differential geometry in its foundations provides approximations of local phenomena through infinitesimal or differential constructions. Here, all equations are linear. If one wants to consider global aspects, however, usually the presence of curvature leads to a nonlinearity in the equations. The simplest case is the one of geodesics which are described by a system of second order nonlinear ODE; their linearizations are the Jacobi fields. More recently, nonlinear PDE played a more and more prominent role in geometry. Let us list some of the most important ones: - harmonic maps between Riemannian and Kahlerian manifolds - minimal surfaces in Riemannian manifolds - Monge-Ampere equations on Kahler manifolds - Yang-Mills equations in vector bundles over manifolds. While the solution of these equations usually is nontrivial, it can lead to very signifi cant results in geometry, as solutions provide maps, submanifolds, metrics, or connections which are distinguished by geometric properties in a given context. All these equations are elliptic, but often parabolic equations are used as an auxiliary tool to solve the elliptic ones.
Download or read book An Introduction to Extremal Kahler Metrics written by Gábor Székelyhidi and published by American Mathematical Soc.. This book was released on 2014-06-19 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.
Download or read book Lectures on K hler Geometry written by Andrei Moroianu and published by Cambridge University Press. This book was released on 2007-03-29 with total page 4 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.
Download or read book Complex Geometry written by Daniel Huybrechts and published by Springer Science & Business Media. This book was released on 2005 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Easily accessible Includes recent developments Assumes very little knowledge of differentiable manifolds and functional analysis Particular emphasis on topics related to mirror symmetry (SUSY, Kaehler-Einstein metrics, Tian-Todorov lemma)
Download or read book Canonical Metrics in K hler Geometry written by Gang Tian and published by Birkhäuser. This book was released on 2012-12-06 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been fundamental progress in complex differential geometry in the last two decades. For one, The uniformization theory of canonical Kähler metrics has been established in higher dimensions, and many applications have been found, including the use of Calabi-Yau spaces in superstring theory. This monograph gives an introduction to the theory of canonical Kähler metrics on complex manifolds. It also presents some advanced topics not easily found elsewhere.
Download or read book Differential Analysis on Complex Manifolds written by Raymond O. Wells and published by Springer Science & Business Media. This book was released on 2007-10-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.
Download or read book Iterated Integrals And Cycles On Algebraic Manifolds written by Bruno Harris and published by World Scientific. This book was released on 2004-03-15 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This subject has been of great interest both to topologists and to number theorists. The first part of this book describes some of the work of Kuo-Tsai Chen on iterated integrals and the fundamental group of a manifold. The author attempts to make his exposition accessible to beginning graduate students. He then proceeds to apply Chen's constructions to algebraic geometry, showing how this leads to some results on algebraic cycles and the Abel-Jacobi homomorphism. Finally, he presents a more general point of view relating Chen's integrals to a generalization of the concept of linking numbers, and ends up with a new invariant of homology classes in a projective algebraic manifold. The book is based on a course given by the author at the Nankai Institute of Mathematics in the fall of 2001.
Download or read book The Geometry of Hessian Structures written by Hirohiko Shima and published by World Scientific. This book was released on 2007 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Khlerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the theory.
Download or read book Chern Numbers And Rozansky witten Invariants Of Compact Hyper kahler Manifolds written by Marc Nieper-wisskirchen and published by World Scientific. This book was released on 2004-06-22 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book deals with the theory of Rozansky-Witten invariants, introduced by L Rozansky and E Witten in 1997. It covers the latest developments in an area where research is still very active and promising. With a chapter on compact hyper-Kähler manifolds, the book includes a detailed discussion on the applications of the general theory to the two main example series of compact hyper-Kähler manifolds: the Hilbert schemes of points on a K3 surface and the generalized Kummer varieties.
Download or read book Symplectic Manifolds with no Kaehler structure written by Alesky Tralle and published by Springer. This book was released on 2006-11-14 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2019-08-19 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications.
Download or read book Infinite Dimensional K hler Manifolds written by Alan Huckleberry and published by Birkhäuser. This book was released on 2012-12-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite dimensional manifolds, Lie groups and algebras arise naturally in many areas of mathematics and physics. Having been used mainly as a tool for the study of finite dimensional objects, the emphasis has changed and they are now frequently studied for their own independent interest. On the one hand this is a collection of closely related articles on infinite dimensional Kähler manifolds and associated group actions which grew out of a DMV-Seminar on the same subject. On the other hand it covers significantly more ground than was possible during the seminar in Oberwolfach and is in a certain sense intended as a systematic approach which ranges from the foundations of the subject to recent developments. It should be accessible to doctoral students and as well researchers coming from a wide range of areas. The initial chapters are devoted to a rather selfcontained introduction to group actions on complex and symplectic manifolds and to Borel-Weil theory in finite dimensions. These are followed by a treatment of the basics of infinite dimensional Lie groups, their actions and their representations. Finally, a number of more specialized and advanced topics are discussed, e.g., Borel-Weil theory for loop groups, aspects of the Virasoro algebra, (gauge) group actions and determinant bundles, and second quantization and the geometry of the infinite dimensional Grassmann manifold.
Download or read book Library of Congress Subject Headings written by Library of Congress and published by . This book was released on 2013 with total page 1480 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Library of Congress Subject Headings P Z written by Library of Congress. Subject Cataloging Division and published by . This book was released on 1988 with total page 1436 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Selected Works of Ilya Piatetski Shapiro written by James Cogdell and published by American Mathematical Society. This book was released on 2022-11-03 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: This selection of papers of I. Piatetski-Shapiro represents almost 50 years of his mathematical activity. Included are many of his major papers in harmonic analysis, number theory, discrete groups, bounded homogeneous domains, algebraic geometry, automorphic forms, and automorphic $L$-functions. The papers in the volume are intended as a representative and accurate reflection of both the breadth and depth of Piatetski-Shapiro's work in mathematics. Some of his early works, such as those on the prime number theorem and on sets of uniqueness for trigonometric series, appear for the first time in English. Also included are several commentaries by his close colleagues. This volume offers an elegant representation of the contributions made by this renowned mathematician.
