Infinite Dimensional Kähler Manifolds

Author : Alan Huckleberry,Tilmann Wurzbacher
Publisher : Birkhäuser
Page : 385 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034882279

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Infinite Dimensional Kähler Manifolds by Alan Huckleberry,Tilmann Wurzbacher Pdf

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.

Author : Alan T. Huckleberry,Tilman Wurzbacher
Publisher : Birkhauser
Page : 375 pages
File Size : 53,5 Mb
Release : 2001-01-01
Category : Kählerian manifolds
ISBN : 0817666028

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Infinite Dimensional Kähler Manifolds by Alan T. Huckleberry,Tilman Wurzbacher Pdf

Author : Andrea Loi,Michela Zedda
Publisher : Springer
Page : 100 pages
File Size : 48,6 Mb
Release : 2018-09-20
Category : Mathematics
ISBN : 9783319994833

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Kähler Immersions of Kähler Manifolds into Complex Space Forms by Andrea Loi,Michela Zedda Pdf

The aim of this book is to describe Calabi's original work on Kähler immersions of Kähler manifolds into complex space forms, to provide a detailed account of what is known today on the subject and to point out some open problems. Calabi's pioneering work, making use of the powerful tool of the diastasis function, allowed him to obtain necessary and sufficient conditions for a neighbourhood of a point to be locally Kähler immersed into a finite or infinite-dimensional complex space form. This led to a classification of (finite-dimensional) complex space forms admitting a Kähler immersion into another, and to decades of further research on the subject. Each chapter begins with a brief summary of the topics to be discussed and ends with a list of exercises designed to test the reader's understanding. Apart from the section on Kähler immersions of homogeneous bounded domains into the infinite complex projective space, which could be skipped without compromising the understanding of the rest of the book, the prerequisites to read this book are a basic knowledge of complex and Kähler geometry.

Author : Victor Kac
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211044

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Infinite Dimensional Groups with Applications by Victor Kac Pdf

This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.

Author : Armen Sergeev
Publisher : Mathematical Society Of Japan Memoirs
Page : 212 pages
File Size : 51,6 Mb
Release : 2010-05
Category : Mathematics
ISBN : 4931469604

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Kahler geometry of loop spaces by Armen Sergeev Pdf

In this book we study three important classes of infinite-dimensional KÄhler manifolds - loop spaces of compact Lie groups, TeichmÜller spaces of complex structures on loop spaces, and Grassmannians of Hilbert spaces. Each of these manifolds has a rich KÄhler geometry, considered in the first part of the book, and may be considered as a universal object in a category, containing all its finite-dimensional counterparts. On the other hand, these manifolds are closely related to string theory. This motivates our interest in their geometric quantization presented in the second part of the book together with a brief survey of geometric quantization of finite-dimensional KÄhler manifolds. The book is provided with an introductory chapter containing basic notions on infinite-dimensional Frechet manifolds and Frechet Lie groups. It can also serve as an accessible introduction to KÄhler geometry of infinite-dimensional complex manifolds with special attention to the aforementioned three particular classes. It may be interesting for mathematicians working with infinite-dimensional complex manifolds and physicists dealing with string theory. Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

Author : Tilmann Wurzbacher
Publisher : Walter de Gruyter
Page : 259 pages
File Size : 47,7 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110200010

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Infinite Dimensional Groups and Manifolds by Tilmann Wurzbacher Pdf

The volume is a collection of refereed research papers on infinite dimensional groups and manifolds in mathematics and quantum physics. Topics covered are: new classes of Lie groups of mappings, the Burgers equation, the Chern--Weil construction in infinite dimensions, the hamiltonian approach to quantum field theory, and different aspects of large N limits ranging from approximation methods in quantum mechanics to modular forms and string/gauge theory duality. Directed at research mathematicians and theoretical physicists as well as graduate students, the volume gives an overview of important themes of research at the forefront of mathematics and theoretical physics.

Author : Petr P. Kulish,Nenad Manojlovic,Henning Samtleben
Publisher : Springer Science & Business Media
Page : 266 pages
File Size : 43,6 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373412

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Infinite Dimensional Algebras and Quantum Integrable Systems by Petr P. Kulish,Nenad Manojlovic,Henning Samtleben Pdf

This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics. In it, recent developments in the theory of infinite dimensional algebras, and their applications to quantum integrable systems, are reviewed by leading experts in the field.

Author : S.T. Ali,J-P Antoine,W. Lisiecki,I.M. Mladenov,A. Odzijewicz
Publisher : Springer Science & Business Media
Page : 273 pages
File Size : 51,6 Mb
Release : 2013-03-09
Category : Technology & Engineering
ISBN : 9781461525646

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Quantization and Infinite-Dimensional Systems by S.T. Ali,J-P Antoine,W. Lisiecki,I.M. Mladenov,A. Odzijewicz Pdf

As all participants know by now, the Bialowieza Summer Workshop has acquired a life of its own. The charming venue of the meetings, the informal atmosphere, the enthusiasm of the participants and the intensity of the scientific interaction have all conspired to make these meetings wonderful learning experiences. The XIIth Workshop (held from July 1 - 7, 1993) was once again a topical meeting within the general area of Differential Geometric Methods in Physics, focusing specifically on Quantization and Infinite-dimensional Systems. Altogether, about fifty participants attended the workshop. As before, the aim of the workshop was to have a small number of in-depth lectures on the main theme and a somewhat larger number of short presentations on related areas, while leaving enough free time for private discussions and exchange of ideas. Topics treated in the workshop included field theory, geometric quantization and symplectic geometry, coherent states methods, holomorphic representation theory, Poisson structures, non-commutative geometry, supersymmetry and quantum groups. The editors have the pleasant task of first thanking all the local organizers, in particular Dr. K. Gilewicz, for their painstaking efforts in ensuring the smooth running of the meeting and for organizing a delightful array of social events. Secondly, they would like to record their indebtedness to all the people who have contributed to this volume and to the redoubtable Ms. Cindy Parkinson without whose patient typesetting and editing skills the volume could hardly have seen the light of the day.

Author : Vincent Guedj
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 55,8 Mb
Release : 2012-01-06
Category : Mathematics
ISBN : 9783642236686

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Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics by Vincent Guedj Pdf

The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong–Sturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis.

Author : Richard S. Palais
Publisher : Unknown
Page : 390 pages
File Size : 49,7 Mb
Release : 1965
Category : Differential topology
ISBN : UVA:X001468429

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Lectures on the Differential Topology of Infinite Dimensional Manifolds by Richard S. Palais Pdf

Author : Karl-Hermann Neeb,Arturo Pianzola
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 43,8 Mb
Release : 2010-10-17
Category : Mathematics
ISBN : 9780817647414

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Developments and Trends in Infinite-Dimensional Lie Theory by Karl-Hermann Neeb,Arturo Pianzola Pdf

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.

Author : Victor Kac
Publisher : Unknown
Page : 396 pages
File Size : 49,6 Mb
Release : 1985-10-14
Category : Electronic
ISBN : 1461211050

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Infinite Dimensional Groups with Applications by Victor Kac Pdf

Author : Hirotaka Tamanoi
Publisher : Springer
Page : 397 pages
File Size : 49,9 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540487883

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Elliptic Genera and Vertex Operator Super-Algebras by Hirotaka Tamanoi Pdf

This monograph deals with two aspects of the theory of elliptic genus: its topological aspect involving elliptic functions, and its representation theoretic aspect involving vertex operator super-algebras. For the second aspect, elliptic genera are shown to have the structure of modules over certain vertex operator super-algebras. The vertex operators corresponding to parallel tensor fields on closed Riemannian Spin Kähler manifolds such as Riemannian tensors and Kähler forms are shown to give rise to Virasoro algebras and affine Lie algebras. This monograph is chiefly intended for topologists and it includes accounts on topics outside of topology such as vertex operator algebras.

Author : Werner Ballmann
Publisher : European Mathematical Society
Page : 190 pages
File Size : 53,8 Mb
Release : 2006
Category : Mathematics
ISBN : 3037190256

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Lectures on Kähler Manifolds by Werner Ballmann Pdf

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.

Author : Robert Geroch
Publisher : Minkowski Institute Press
Page : 137 pages
File Size : 49,9 Mb
Release : 2013-12-16
Category : Mathematics
ISBN : 9781927763162

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Infinite-Dimensional Manifolds by Robert Geroch Pdf

Robert Geroch's lecture notes "Infinite-Dimensional Manifolds" provide a concise, clear, and helpful introduction to a wide range of subjects, which are essential in mathematical and theoretical physics - Banach spaces, open mapping theorem, splitting, bounded linear mappings, derivatives, mean value theorem, manifolds, mappings of manifolds, scalar and vector fields, tensor products, tensor spaces, natural tensors, tensor fields, tensor bundles, Lie derivatives, integral curves, geometry of Lie derivatives, exterior derivatives, derivative operators, partial differential equations, and Riemannian geometry. Like in his other books, Geroch explains even the most abstract concepts with the help of intuitive examples and many (over 60) figures. Like Geroch's other books, this book too can be used for self-study since each chapter contains examples plus a set of problems given in the Appendix.