Kahler Einstein Metrics And Integral Invariants

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Kähler-Einstein Metrics and Integral Invariants

Author : Akito Futaki
Publisher : Springer
ISBN 13 : 354039172X
Total Pages : 145 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Kähler-Einstein Metrics and Integral Invariants by : Akito Futaki

Download or read book Kähler-Einstein Metrics and Integral Invariants written by Akito Futaki and published by Springer. This book was released on 2006-11-15 with total page 145 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present very recent results on compact Kähler-Einstein manifolds of positive scalar curvature. A central role is played here by a Lie algebra character of the complex Lie algebra consisting of all holomorphic vector fields, which can be intrinsically defined on any compact complex manifold and becomes an obstruction to the existence of a Kähler-Einstein metric. Recent results concerning this character are collected here, dealing with its origin, generalizations, sufficiency for the existence of a Kähler-Einstein metric and lifting to a group character. Other related topics such as extremal Kähler metrics studied by Calabi and others and the existence results of Tian and Yau are also reviewed. As the rudiments of Kählerian geometry and Chern-Simons theory are presented in full detail, these notes are accessible to graduate students as well as to specialists of the subject.

Kahler-Einstein Metrics and Integral Invariants

Author : Akito Futaki
Publisher :
ISBN 13 : 9783662207192
Total Pages : 148 pages
Book Rating : 4.2/5 (71 download)

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Book Synopsis Kahler-Einstein Metrics and Integral Invariants by : Akito Futaki

Download or read book Kahler-Einstein Metrics and Integral Invariants written by Akito Futaki and published by . This book was released on 2014-09-01 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Kahler-Einstein Metrics and Integral Invariants

Author :
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (846 download)

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Book Synopsis Kahler-Einstein Metrics and Integral Invariants by :

Download or read book Kahler-Einstein Metrics and Integral Invariants written by and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation. These notes present very recent results on compact Kähler-Einstein manifolds of positive scalar curvature. A central role is played here by a Lie algebra character of the complex Lie algebra consisting of all holomorphic vector fields, which can be intrinsically defined on any compact complex manifold and becomes an obstruction to the existence of a Kähler-Einstein metric. Recent results concerning this character are collected here, dealing with its origin, generalizations, sufficiency for the existence of a Kähler-Einstein metric and lifting to a group character. Other related topics such as extremal Kähler metrics studied by Calabi and others and the existence results of Tian and Yau are also reviewed. As the rudiments of Kählerian geometry and Chern-Simons theory are presented in full detail, these notes are accessible to graduate students as well as to specialists of the subject.

An Introduction to Extremal Kahler Metrics

Author : Gábor Székelyhidi
Publisher : American Mathematical Soc.
ISBN 13 : 1470410478
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis An Introduction to Extremal Kahler Metrics by : Gábor Székelyhidi

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.

Canonical Metrics in Kähler Geometry

Author : Gang Tian
Publisher : Birkhäuser
ISBN 13 : 3034883897
Total Pages : 107 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Canonical Metrics in Kähler Geometry by : Gang Tian

Download or read book Canonical Metrics in Kähler 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.

Recent Topics in Differential and Analytic Geometry

Author : T. Ochiai
Publisher : Academic Press
ISBN 13 : 1483214680
Total Pages : 462 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Recent Topics in Differential and Analytic Geometry by : T. Ochiai

Download or read book Recent Topics in Differential and Analytic Geometry written by T. Ochiai and published by Academic Press. This book was released on 2014-07-14 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Studies in Pure Mathematics, Volume 18-I: Recent Topics in Differential and Analytic Geometry presents the developments in the field of analytical and differential geometry. This book provides some generalities about bounded symmetric domains. Organized into two parts encompassing 12 chapters, this volume begins with an overview of harmonic mappings and holomorphic foliations. This text then discusses the global structures of a compact Kähler manifold that is locally decomposable as an isometric product of Ricci-positive, Ricci-negative, and Ricci-flat parts. Other chapters consider the most recognized non-standard examples of compact homogeneous Einstein manifolds constructed via Riemannian submersions. This book discusses as well the natural compactification of the moduli space of polarized Einstein–Kähler orbitfold with a given Hilbert polynomials. The final chapter deals with solving a degenerate Monge–Ampère equation by constructing a family of Einstein–Kähler metrics on the smooth part of minimal varieties of general kind. This book is a valuable resource for graduate students and pure mathematicians.

Mathematical Works

Author : Erich Kähler
Publisher : Walter de Gruyter
ISBN 13 : 9783110171181
Total Pages : 986 pages
Book Rating : 4.1/5 (711 download)

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Book Synopsis Mathematical Works by : Erich Kähler

Download or read book Mathematical Works written by Erich Kähler and published by Walter de Gruyter. This book was released on 2003 with total page 986 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most mathematicians and many mathematical physicists the name Erich Kähler is strongly tied to important geometric notions such as Kähler metrics, Kähler manifolds and Kähler groups. They all go back to a paper of 14 pages written in 1932. This, however, is just a small part of Kähler's many outstanding achievements which cover an unusually wide area: From celestial mechanics he got into complex function theory, differential equations, analytic and complex geometry with differential forms, and then into his main topic, i.e. arithmetic geometry where he constructed a system of notions which is a precursor and, in large parts, equivalent to the now used system of Grothendieck and Dieudonné. His principal interest was in finding the unity in the variety of mathematical themes and establishing thus mathematics as a universal language. In this volume Kähler's mathematical papers are collected following a "Tribute to Herrn Erich Kähler" by S. S. Chern, an overview of Kähler's life data by A. Bohm and R. Berndt, and a Survey of his Mathematical Work by the editors. There are also comments and reports on the developments of the main topics of Kähler's work, starting by W. Neumann's paper on the topology of hypersurface singularities, J.-P. Bourguignon's report on Kähler geometry and, among others by Berndt, Bost, Deitmar, Ekeland, Kunz and Krieg, up to A. Nicolai's essay "Supersymmetry, Kähler geometry and Beyond". As Kähler's interest went beyond the realm of mathematics and mathematical physics, any picture of his work would be incomplete without touching his work reaching into other regions. So a short appendix reproduces three of his articles concerning his vision of mathematics as a universal Theme together with an essay by K. Maurin giving an "Approach to the philosophy of Erich Kähler".

Selected Papers on Number Theory, Algebraic Geometry, and Differential Geometry

Author : Katsumi Nomizu
Publisher : American Mathematical Soc.
ISBN 13 : 9780821875117
Total Pages : 170 pages
Book Rating : 4.8/5 (751 download)

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Book Synopsis Selected Papers on Number Theory, Algebraic Geometry, and Differential Geometry by : Katsumi Nomizu

Download or read book Selected Papers on Number Theory, Algebraic Geometry, and Differential Geometry written by Katsumi Nomizu and published by American Mathematical Soc.. This book was released on 1994 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents papers that originally appeared in the Japanese journal Sugaku. The papers explore the relationship between number theory, algebraic geometry, and differential geometry.

Fifth International Congress of Chinese Mathematicians

Author : Lizhen Ji
Publisher : American Mathematical Soc.
ISBN 13 : 0821875868
Total Pages : 520 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fifth International Congress of Chinese Mathematicians by : Lizhen Ji

Download or read book Fifth International Congress of Chinese Mathematicians written by Lizhen Ji and published by American Mathematical Soc.. This book was released on 2012 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Existence of Extremal Kahler Metrics on Compact Complex Manifolds, and a Partial Converse to a Theorem of Lichnerowicz

Author : Andrew David Hwang
Publisher :
ISBN 13 :
Total Pages : 108 pages
Book Rating : 4.:/5 (33 download)

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Book Synopsis Existence of Extremal Kahler Metrics on Compact Complex Manifolds, and a Partial Converse to a Theorem of Lichnerowicz by : Andrew David Hwang

Download or read book Existence of Extremal Kahler Metrics on Compact Complex Manifolds, and a Partial Converse to a Theorem of Lichnerowicz written by Andrew David Hwang and published by . This book was released on 1993 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Kähler Manifolds

Author : Werner Ballmann
Publisher : European Mathematical Society
ISBN 13 : 9783037190258
Total Pages : 190 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis Lectures on Kähler Manifolds by : Werner Ballmann

Download or read book Lectures on Kähler 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.

Kähler-Einstein Metrics on Products

Author : Greg Weyland Howell
Publisher :
ISBN 13 :
Total Pages : 68 pages
Book Rating : 4.:/5 (328 download)

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Book Synopsis Kähler-Einstein Metrics on Products by : Greg Weyland Howell

Download or read book Kähler-Einstein Metrics on Products written by Greg Weyland Howell and published by . This book was released on 1994 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics

Author : Yum-Tong Siu
Publisher :
ISBN 13 :
Total Pages : 171 pages
Book Rating : 4.:/5 (53 download)

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Book Synopsis Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics by : Yum-Tong Siu

Download or read book Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics written by Yum-Tong Siu and published by . This book was released on 1987 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Selected Papers of Weiyue Ding

Author : You-De Wang
Publisher : World Scientific Publishing Company
ISBN 13 : 9789813220874
Total Pages : 632 pages
Book Rating : 4.2/5 (28 download)

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Book Synopsis Selected Papers of Weiyue Ding by : You-De Wang

Download or read book Selected Papers of Weiyue Ding written by You-De Wang and published by World Scientific Publishing Company. This book was released on 2018 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: 49 papers of the professor and member of the Chinese Academy of Sciences, particularly on differential equations and geometric analysis.

Geometric Analysis

Author : Jingyi Chen
Publisher : Springer Nature
ISBN 13 : 3030349535
Total Pages : 616 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Geometric Analysis by : Jingyi Chen

Download or read book Geometric Analysis written by Jingyi Chen and published by Springer Nature. This book was released on 2020-04-10 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume has a two-fold purpose. First, comprehensive survey articles provide a way for beginners to ease into the corresponding sub-fields. These are then supplemented by original works that give the more advanced readers a glimpse of the current research in geometric analysis and related PDEs. The book is of significant interest for researchers, including advanced Ph.D. students, working in geometric analysis. Readers who have a secondary interest in geometric analysis will benefit from the survey articles. The results included in this book will stimulate further advances in the subjects: geometric analysis, including complex differential geometry, symplectic geometry, PDEs with a geometric origin, and geometry related to topology. Contributions by Claudio Arezzo, Alberto Della Vedova, Werner Ballmann, Henrik Matthiesen, Panagiotis Polymerakis, Sun-Yung A. Chang, Zheng-Chao Han, Paul Yang, Tobias Holck Colding, William P. Minicozzi II, Panagiotis Dimakis, Richard Melrose, Akito Futaki, Hajime Ono, Jiyuan Han, Jeff A. Viaclovsky, Bruce Kleiner, John Lott, Sławomir Kołodziej, Ngoc Cuong Nguyen, Chi Li, Yuchen Liu, Chenyang Xu, YanYan Li, Luc Nguyen, Bo Wang, Shiguang Ma, Jie Qing, Xiaonan Ma, Sean Timothy Paul, Kyriakos Sergiou, Tristan Rivière, Yanir A. Rubinstein, Natasa Sesum, Jian Song, Jeffrey Streets, Neil S. Trudinger, Yu Yuan, Weiping Zhang, Xiaohua Zhu and Aleksey Zinger.

An Introduction to the Kähler-Ricci Flow

Author : Sebastien Boucksom
Publisher : Springer
ISBN 13 : 3319008196
Total Pages : 342 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis An Introduction to the Kähler-Ricci Flow by : Sebastien Boucksom

Download or read book An Introduction to the Kähler-Ricci Flow written by Sebastien Boucksom and published by Springer. This book was released on 2013-10-02 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects lecture notes from courses offered at several conferences and workshops, and provides the first exposition in book form of the basic theory of the Kähler-Ricci flow and its current state-of-the-art. While several excellent books on Kähler-Einstein geometry are available, there have been no such works on the Kähler-Ricci flow. The book will serve as a valuable resource for graduate students and researchers in complex differential geometry, complex algebraic geometry and Riemannian geometry, and will hopefully foster further developments in this fascinating area of research. The Ricci flow was first introduced by R. Hamilton in the early 1980s, and is central in G. Perelman’s celebrated proof of the Poincaré conjecture. When specialized for Kähler manifolds, it becomes the Kähler-Ricci flow, and reduces to a scalar PDE (parabolic complex Monge-Ampère equation). As a spin-off of his breakthrough, G. Perelman proved the convergence of the Kähler-Ricci flow on Kähler-Einstein manifolds of positive scalar curvature (Fano manifolds). Shortly after, G. Tian and J. Song discovered a complex analogue of Perelman’s ideas: the Kähler-Ricci flow is a metric embodiment of the Minimal Model Program of the underlying manifold, and flips and divisorial contractions assume the role of Perelman’s surgeries.

Geometry and Physics

Author : H. Pedersen
Publisher : CRC Press
ISBN 13 : 1000110850
Total Pages : 766 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Geometry and Physics by : H. Pedersen

Download or read book Geometry and Physics written by H. Pedersen and published by CRC Press. This book was released on 2021-01-07 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on the proceedings of the Special Session on Geometry and Physics held over a six month period at the University of Aarhus, Denmark and on articles from the Summer school held at Odense University, Denmark. Offers new contributions on a host of topics that involve physics, geometry, and topology. Written by more than 50 leading international experts."