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Author : Paul Schwahn
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (139 download)
Download or read book Stability of Einstein metrics on homogeneous spaces written by Paul Schwahn and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. E. D'Atri
Publisher : American Mathematical Soc.
ISBN 13 : 9780821859667
Total Pages : 80 pages
Book Rating : 4.8/5 (596 download)
Download or read book Naturally Reductive Metrics and Einstein Metrics on Compact Lie Groups written by J. E. D'Atri and published by American Mathematical Soc.. This book was released on 1979-12-31 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : Megan M. Kerr
Publisher :
ISBN 13 :
Total Pages : 106 pages
Book Rating : 4.:/5 (776 download)
Download or read book Homogeneous Einstein Metrics written by Megan M. Kerr and published by . This book was released on 1995 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Owen Dearricott
Publisher : Cambridge University Press
ISBN 13 : 1108812813
Total Pages : 401 pages
Book Rating : 4.1/5 (88 download)
Download or read book Differential Geometry in the Large written by Owen Dearricott and published by Cambridge University Press. This book was released on 2020-10-22 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Ricci flow to GIT, physics to curvature bounds, Sasaki geometry to almost formality. This is differential geometry at large.
Author : Fatima Araujo
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (827 download)
Download or read book Einstein Homogeneous Riemannian Fibrations written by Fatima Araujo and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is dedicated to the study of the existence of homogeneous Einstein metrics on the total space of homogeneous fibrations such that the fibers are totally geodesic manifolds. We obtain the Ricci curvature of an invariant metric with totally geodesic fibers and some necessary conditions for the existence of Einstein metrics with totally geodesic fibers in terms of Casimir operators. Some particular cases are studied, for instance, for normal base or fiber, symmetric fiber, Einstein base or fiber, for which the Einstein equations are manageable. We investigate the existence of such Einstein metrics for invariant bisymmetric fibrations of maximal rank, i.e., when both the base and the fiber are symmetric spaces and the base is an isotropy irreducible space of maximal rank. We find this way new Einstein metrics. For such spaces we describe explicitly the isotropy representation in terms subsets of roots and compute the eigenvalues of the Casimir operators of the fiber along the horizontal direction. Results for compact simply connected 4-symmetric spaces of maximal rank follow from this. Also, new invariant Einstein metrics are found on Kowalski n-symmetric spaces.
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 : Ivan Cheltsov
Publisher : Springer Nature
ISBN 13 : 3031178599
Total Pages : 882 pages
Book Rating : 4.0/5 (311 download)
Download or read book Birational Geometry, Kähler–Einstein Metrics and Degenerations written by Ivan Cheltsov and published by Springer Nature. This book was released on 2023-05-23 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects the proceedings of a series of conferences dedicated to birational geometry of Fano varieties held in Moscow, Shanghai and Pohang The conferences were focused on the following two related problems: • existence of Kähler–Einstein metrics on Fano varieties • degenerations of Fano varieties on which two famous conjectures were recently proved. The first is the famous Borisov–Alexeev–Borisov Conjecture on the boundedness of Fano varieties, proved by Caucher Birkar (for which he was awarded the Fields medal in 2018), and the second one is the (arguably even more famous) Tian–Yau–Donaldson Conjecture on the existence of Kähler–Einstein metrics on (smooth) Fano varieties and K-stability, which was proved by Xiuxiong Chen, Sir Simon Donaldson and Song Sun. The solutions for these longstanding conjectures have opened new directions in birational and Kähler geometries. These research directions generated new interesting mathematical problems, attracting the attention of mathematicians worldwide. These conferences brought together top researchers in both fields (birational geometry and complex geometry) to solve some of these problems and understand the relations between them. The result of this activity is collected in this book, which contains contributions by sixty nine mathematicians, who contributed forty three research and survey papers to this volume. Many of them were participants of the Moscow–Shanghai–Pohang conferences, while the others helped to expand the research breadth of the volume—the diversity of their contributions reflects the vitality of modern Algebraic Geometry.
Author : Mauro Carfora
Publisher : Springer Nature
ISBN 13 : 9811985405
Total Pages : 181 pages
Book Rating : 4.8/5 (119 download)
Download or read book Einstein Constraints and Ricci Flow written by Mauro Carfora and published by Springer Nature. This book was released on 2023-01-10 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike.
Author : Jochen Brüning
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110451530
Total Pages : 590 pages
Book Rating : 4.1/5 (14 download)
Download or read book Space – Time – Matter written by Jochen Brüning and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-04-09 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph describes some of the most interesting results obtained by the mathematicians and physicists collaborating in the CRC 647 "Space – Time – Matter", in the years 2005 - 2016. The work presented concerns the mathematical and physical foundations of string and quantum field theory as well as cosmology. Important topics are the spaces and metrics modelling the geometry of matter, and the evolution of these geometries. The partial differential equations governing such structures and their singularities, special solutions and stability properties are discussed in detail. Contents Introduction Algebraic K-theory, assembly maps, controlled algebra, and trace methods Lorentzian manifolds with special holonomy – Constructions and global properties Contributions to the spectral geometry of locally homogeneous spaces On conformally covariant differential operators and spectral theory of the holographic Laplacian Moduli and deformations Vector bundles in algebraic geometry and mathematical physics Dyson–Schwinger equations: Fix-point equations for quantum fields Hidden structure in the form factors ofN = 4 SYM On regulating the AdS superstring Constraints on CFT observables from the bootstrap program Simplifying amplitudes in Maxwell-Einstein and Yang-Mills-Einstein supergravities Yangian symmetry in maximally supersymmetric Yang-Mills theory Wave and Dirac equations on manifolds Geometric analysis on singular spaces Singularities and long-time behavior in nonlinear evolution equations and general relativity
Author : Richard Heiner Bamler
Publisher :
ISBN 13 :
Total Pages : 374 pages
Book Rating : 4.:/5 (732 download)
Download or read book Stability of Einstein Metrics of Negative Curvature written by Richard Heiner Bamler and published by . This book was released on 2011 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Toshiki Mabuchi
Publisher : CRC Press
ISBN 13 : 9780824790691
Total Pages : 244 pages
Book Rating : 4.7/5 (96 download)
Download or read book Einstein Metrics and Yang-Mills Connections written by Toshiki Mabuchi and published by CRC Press. This book was released on 1993-04-20 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers presented at the 27th Taniguchi International Symposium, held in Sanda, Japan - focusing on the study of moduli spaces of various geometric objects such as Einstein metrics, conformal structures, and Yang-Mills connections from algebraic and analytic points of view.;Written by over 15 authorities from around the world, Einstein Metrics and Yang-Mills Connections...: discusses current topics in Kaehler geometry, including Kaehler-Einstein metrics, Hermitian-Einstein connections and a new Kaehler version of Kawamata-Viehweg's vanishing theorem; explores algebraic geometric treatments of holomorphic vector bundles on curves and surfaces; addresses nonlinear problems related to Mong-Ampere and Yamabe-type equations as well as nonlinear equations in mathematical physics; and covers interdisciplinary topics such as twistor theory, magnetic monopoles, KP-equations, Einstein and Gibbons-Hawking metrics, and supercommutative algebras of superdifferential operators.;Providing a wide array of original research articles not published elsewhere Einstein Metrics and Yang-Mills Connections is for research mathematicians, including topologists and differential and algebraic geometers, theoretical physicists, and graudate-level students in these disciplines.
Author : Eric Grinberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821811487
Total Pages : 524 pages
Book Rating : 4.8/5 (218 download)
Download or read book Analysis, Geometry, Number Theory: The Mathematics of Leon Ehrenpreis written by Eric Grinberg and published by American Mathematical Soc.. This book was released on 2000 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the proceedings from the conference honoring the work of Leon Ehrenpreis. Professor Ehrenpreis worked in many different areas of mathematics and found connections among all of them. For example, one can find his analytic ideas in the context of number theory, geometric thinking within analysis, transcendental number theory applied to partial differential equations, and more. The conference brought together the communities of mathematicians working in the areas of interest to Professor Ehrenpreis and allowed them to share the research inspired by his work. The collection of articles here presents current research on PDEs, several complex variables, analytic number theory, integral geometry, and tomography. The work of Professor Ehrenpreis has contributed to basic definitions in these areas and has motivated a wealth of research results. This volume offers a survey of the fundamental principles that unified the conference and influenced the mathematics of Leon Ehrenpreis.
Author : Chaohao Gu
Publisher : World Scientific
ISBN 13 : 9814554405
Total Pages : 349 pages
Book Rating : 4.8/5 (145 download)
Download or read book Differential Geometry - Proceedings Of The Symposium In Honor Of Prof Su Buchin On His 90th Birthday written by Chaohao Gu and published by World Scientific. This book was released on 1993-02-04 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topics covered in this volume are global differential geometry and its application to physics. Recent results in many areas are presented, including Yang-Mills fields, harmonic maps, geometry of submanifolds, spectral geometry, complex geometry and soliton aspects of nonlinear PDE arising from geometry and mathematical physics.
Author : Demetrios Christodoulou
Publisher : Princeton University Press
ISBN 13 : 1400863171
Total Pages : 525 pages
Book Rating : 4.4/5 (8 download)
Download or read book The Global Nonlinear Stability of the Minkowski Space (PMS-41) written by Demetrios Christodoulou and published by Princeton University Press. This book was released on 2014-07-14 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this work is to provide a proof of the nonlinear gravitational stability of the Minkowski space-time. More precisely, the book offers a constructive proof of global, smooth solutions to the Einstein Vacuum Equations, which look, in the large, like the Minkowski space-time. In particular, these solutions are free of black holes and singularities. The work contains a detailed description of the sense in which these solutions are close to the Minkowski space-time, in all directions. It thus provides the mathematical framework in which we can give a rigorous derivation of the laws of gravitation proposed by Bondi. Moreover, it establishes other important conclusions concerning the nonlinear character of gravitational radiation. The authors obtain their solutions as dynamic developments of all initial data sets, which are close, in a precise manner, to the flat initial data set corresponding to the Minkowski space-time. They thus establish the global dynamic stability of the latter. Originally published in 1994. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author : Robert Coquereaux
Publisher : World Scientific
ISBN 13 : 9789971504274
Total Pages : 364 pages
Book Rating : 4.5/5 (42 download)
Download or read book Riemannian Geometry, Fiber Bundles, Kaluza-Klein Theories and All That.... written by Robert Coquereaux and published by World Scientific. This book was released on 1988 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the geometrical aspects of Kaluza-Klein theories. The ten chapters cover topics from the differential and Riemannian manifolds to the reduction of Einstein-Yang-Mills action. It would definitely prove interesting reading to physicists and mathematicians, theoretical and experimental.
Author : Martin Lbke
Publisher : World Scientific
ISBN 13 : 9789810221683
Total Pages : 268 pages
Book Rating : 4.2/5 (216 download)
Download or read book The Kobayashi-Hitchin Correspondence written by Martin Lbke and published by World Scientific. This book was released on 1995 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: By the Kobayashi-Hitchin correspondence, the authors of this book mean the isomorphy of the moduli spaces Mst of stable holomorphic resp. MHE of irreducible Hermitian-Einstein structures in a differentiable complex vector bundle on a compact complex manifold. They give a complete proof of this result in the most general setting, and treat several applications and some new examples.After discussing the stability concept on arbitrary compact complex manifolds in Chapter 1, the authors consider, in Chapter 2, Hermitian-Einstein structures and prove the stability of irreducible Hermitian-Einstein bundles. This implies the existence of a natural map I from MHE to Mst which is bijective by the result of (the rather technical) Chapter 3. In Chapter 4 the moduli spaces involved are studied in detail, in particular it is shown that their natural analytic structures are isomorphic via I. Also a comparison theorem for moduli spaces of instantons resp. stable bundles is proved; this is the form in which the Kobayashi-Hitchin has been used in Donaldson theory to study differentiable structures of complex surfaces. The fact that I is an isomorphism of real analytic spaces is applied in Chapter 5 to show the openness of the stability condition and the existence of a natural Hermitian metric in the moduli space, and to study, at least in some cases, the dependence of Mst on the base metric used to define stability. Another application is a rather simple proof of Bogomolov's theorem on surfaces of type VI0. In Chapter 6, some moduli spaces of stable bundles are calculated to illustrate what can happen in the general (i.e. not necessarily Kahler) case compared to the algebraic or Kahler one. Finally, appendices containing results, especially from Hermitian geometry and analysis, in the form they are used in the main part of the book are included."
