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Author : Wakako Obata
Publisher :
ISBN 13 :
Total Pages : 148 pages
Book Rating : 4.3/5 (91 download)
Download or read book Homogeneous Kähler Einstein Manifolds of Nonpositive Curvature Operator written by Wakako Obata and published by . This book was released on 2007 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Gábor Székelyhidi
Publisher : American Mathematical Soc.
ISBN 13 : 1470410478
Total Pages : 210 pages
Book Rating : 4.4/5 (74 download)
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.
Author : Arthur L. Besse
Publisher : Springer Science & Business Media
ISBN 13 : 3540741208
Total Pages : 529 pages
Book Rating : 4.5/5 (47 download)
Download or read book Einstein Manifolds written by Arthur L. Besse and published by Springer Science & Business Media. This book was released on 2007-12-03 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. This is the first book which presents an overview of several striking results ensuing from the examination of Einstein’s equations in the context of Riemannian manifolds. Parts of the text can be used as an introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.
Author : Werner Ballmann
Publisher : European Mathematical Society
ISBN 13 : 9783037190258
Total Pages : 190 pages
Book Rating : 4.1/5 (92 download)
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.
Author : Katsuhiro Shiohama
Publisher : Springer
ISBN 13 : 3540388273
Total Pages : 343 pages
Book Rating : 4.5/5 (43 download)
Download or read book Curvature and Topology of Riemannian Manifolds written by Katsuhiro Shiohama and published by Springer. This book was released on 2006-11-14 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Sebastien Boucksom
Publisher : Springer
ISBN 13 : 3319008196
Total Pages : 342 pages
Book Rating : 4.3/5 (19 download)
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.
Author : Werner Ballmann
Publisher : Birkhäuser
ISBN 13 : 3034892403
Total Pages : 114 pages
Book Rating : 4.0/5 (348 download)
Download or read book Lectures on Spaces of Nonpositive Curvature written by Werner Ballmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory.
Author : Arthur L. Besse
Publisher : Springer
ISBN 13 : 3540743111
Total Pages : 523 pages
Book Rating : 4.5/5 (47 download)
Download or read book Einstein Manifolds written by Arthur L. Besse and published by Springer. This book was released on 2007-11-12 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. This is the first book which presents an overview of several striking results ensuing from the examination of Einstein’s equations in the context of Riemannian manifolds. Parts of the text can be used as an introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.
Author : Oldrich Kowalski
Publisher : Springer Science & Business Media
ISBN 13 : 0817644245
Total Pages : 277 pages
Book Rating : 4.8/5 (176 download)
Download or read book Complex, Contact and Symmetric Manifolds written by Oldrich Kowalski and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Contains research and survey articles by well known and respected mathematicians on recent developments and research trends in differential geometry and topology * Dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields * Papers include all necessary introductory and contextual material to appeal to non-specialists, as well as researchers and differential geometers
Author : Jurgen Berndt
Publisher : CRC Press
ISBN 13 : 1482245167
Total Pages : 494 pages
Book Rating : 4.4/5 (822 download)
Download or read book Submanifolds and Holonomy written by Jurgen Berndt and published by CRC Press. This book was released on 2016-02-22 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Submanifolds and Holonomy, Second Edition explores recent progress in the submanifold geometry of space forms, including new methods based on the holonomy of the normal connection. This second edition reflects many developments that have occurred since the publication of its popular predecessor.New to the Second EditionNew chapter on normal holonom
Author : Eric Boeckx
Publisher : World Scientific
ISBN 13 : 981022768X
Total Pages : 319 pages
Book Rating : 4.8/5 (12 download)
Download or read book Riemannian Manifolds of Conullity Two written by Eric Boeckx and published by World Scientific. This book was released on 1996 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with Riemannian manifolds for which the nullity space of the curvature tensor has codimension two. These manifolds are ?semi-symmetric spaces foliated by Euclidean leaves of codimension two? in the sense of Z I Szab¢. The authors concentrate on the rich geometrical structure and explicit descriptions of these remarkable spaces. Also parallel theories are developed for manifolds of ?relative conullity two?. This makes a bridge to a survey on curvature homogeneous spaces introduced by I M Singer. As an application of the main topic, interesting hypersurfaces with type number two in Euclidean space are discovered, namely those which are locally rigid or ?almost rigid?. The unifying method is solving explicitly particular systems of nonlinear PDE.
Author : Peter B Gilkey
Publisher : World Scientific
ISBN 13 : 1908979275
Total Pages : 389 pages
Book Rating : 4.9/5 (89 download)
Download or read book The Geometry Of Curvature Homogeneous Pseudo-riemannian Manifolds written by Peter B Gilkey and published by World Scientific. This book was released on 2007-04-26 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pseudo-Riemannian geometry is an active research field not only in differential geometry but also in mathematical physics where the higher signature geometries play a role in brane theory. An essential reference tool for research mathematicians and physicists, this book also serves as a useful introduction to students entering this active and rapidly growing field. The author presents a comprehensive treatment of several aspects of pseudo-Riemannian geometry, including the spectral geometry of the curvature tensor, curvature homogeneity, and Stanilov-Tsankov-Videv theory./a
Author : Peter B. Gilkey
Publisher : World Scientific
ISBN 13 : 9812799699
Total Pages : 316 pages
Book Rating : 4.8/5 (127 download)
Download or read book Geometric Properties of Natural Operators Defined by the Riemann Curvature Tensor written by Peter B. Gilkey and published by World Scientific. This book was released on 2001 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: A central problem in differential geometry is to relate algebraic properties of the Riemann curvature tensor to the underlying geometry of the manifold. The full curvature tensor is in general quite difficult to deal with. This book presents results about the geometric consequences that follow if various natural operators defined in terms of the Riemann curvature tensor (the Jacobi operator, the skew-symmetric curvature operator, the Szabo operator, and higher order generalizations) are assumed to have constant eigenvalues or constant Jordan normal form in the appropriate domains of definition. The book presents algebraic preliminaries and various Schur type problems; deals with the skew-symmetric curvature operator in the real and complex settings and provides the classification of algebraic curvature tensors whose skew-symmetric curvature has constant rank 2 and constant eigenvalues; discusses the Jacobi operator and a higher order generalization and gives a unified treatment of the Osserman conjecture and related questions; and establishes the results from algebraic topology that are necessary for controlling the eigenvalue structures. An extensive bibliography is provided. Results are described in the Riemannian, Lorentzian, and higher signature settings, and many families of examples are displayed. Contents: Algebraic Curvature Tensors; The Skew-Symmetric Curvature Operator; The Jacobi Operator; Controlling the Eigenvalue Structure. Readership: Researchers and graduate students in geometry and topology.
Author : Sławomir Dinew
Publisher : Springer Nature
ISBN 13 : 3030258831
Total Pages : 256 pages
Book Rating : 4.0/5 (32 download)
Download or read book Complex Non-Kähler Geometry written by Sławomir Dinew and published by Springer Nature. This book was released on 2019-11-05 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds. The school consisted of four courses, focusing on both the construction of non-Kähler manifolds and the understanding of a possible classification of complex non-Kähler manifolds. In particular, the courses by Alberto Verjovsky and Andrei Teleman introduced tools in the theory of foliations and analytic techniques for the classification of compact complex surfaces and compact Kähler manifolds, respectively. The courses by Sebastien Picard and Sławomir Dinew focused on analytic techniques in Hermitian geometry, more precisely, on special Hermitian metrics and geometric flows, and on pluripotential theory in complex non-Kähler geometry.
Author : Bayram Sahin
Publisher : Academic Press
ISBN 13 : 0128044101
Total Pages : 362 pages
Book Rating : 4.1/5 (28 download)
Download or read book Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications written by Bayram Sahin and published by Academic Press. This book was released on 2017-01-23 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and their Applications is a rich and self-contained exposition of recent developments in Riemannian submersions and maps relevant to complex geometry, focusing particularly on novel submersions, Hermitian manifolds, and K\{a}hlerian manifolds. Riemannian submersions have long been an effective tool to obtain new manifolds and compare certain manifolds within differential geometry. For complex cases, only holomorphic submersions function appropriately, as discussed at length in Falcitelli, Ianus and Pastore's classic 2004 book. In this new book, Bayram Sahin extends the scope of complex cases with wholly new submersion types, including Anti-invariant submersions, Semi-invariant submersions, slant submersions, and Pointwise slant submersions, also extending their use in Riemannian maps. The work obtains new properties of the domain and target manifolds and investigates the harmonicity and geodesicity conditions for such maps. It also relates these maps with discoveries in pseudo-harmonic maps. Results included in this volume should stimulate future research on Riemannian submersions and Riemannian maps. - Systematically reviews and references modern literature in Riemannian maps - Provides rigorous mathematical theory with applications - Presented in an accessible reading style with motivating examples that help the reader rapidly progress
Author : Claude LeBrun
Publisher : American Mathematical Society(RI)
ISBN 13 :
Total Pages : 450 pages
Book Rating : 4.3/5 (91 download)
Download or read book Essays on Einstein Manifolds written by Claude LeBrun and published by American Mathematical Society(RI). This book was released on 1999 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the sixth volume in a series providing surveys of differential geometry. It addresses: Einstein manifolds with zero Ricci curvature; rigidity and compactness of Einstein metrics; general relativity; the stability of Minkowski space-time; and more.
Author : Andrei Moroianu
Publisher : Cambridge University Press
ISBN 13 : 1139463004
Total Pages : 4 pages
Book Rating : 4.1/5 (394 download)
Download or read book Lectures on Kähler 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.
