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.
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.
Download or read book Homogeneous Manifolds with Negative Curvature written by Robert Azencott and published by . This book was released on 1976 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Some Remarks on Rigidity of Einstein Manifolds of Nonpositive Curvature written by Mathematical Sciences Research Institute (Berkeley, Calif.). and published by . This book was released on 1994 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Fredholm Operators and Einstein Metrics on Conformally Compact Manifolds written by John M. Lee and published by American Mathematical Soc.. This book was released on 2006 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main purpose of this monograph is to give an elementary and self-contained account of the existence of asymptotically hyperbolic Einstein metrics with prescribed conformal infinities sufficiently close to that of a given asymptotically hyperbolic Einstein metric with non positive curvature. The proof is based on an elementary derivation of sharp Fredholm theorems for self-adjoint geometric linear elliptic operators on asymptotically hyperbolic manifolds.
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 Non homogeneous K hler Einstein Metrics on Compact Complex Manifolds written by N. Koiso and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Spectral Geometry written by Pierre H. Berard and published by Springer. This book was released on 2006-11-14 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Global Riemannian Geometry written by Thomas Willmore and published by . This book was released on 1984 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transformation Groups in Differential Geometry written by Shoshichi Kobayashi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric struc tures. All geometric structures are not created equal; some are creations of ~ods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geo metric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lec tures I gave in Tokyo and Berkeley in 1965.
Download or read book Geometry of Submanifolds written by Bang-Yen Chen and published by Courier Dover Publications. This book was released on 2019-06-12 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first two chapters of this frequently cited reference provide background material in Riemannian geometry and the theory of submanifolds. Subsequent chapters explore minimal submanifolds, submanifolds with parallel mean curvature vector, conformally flat manifolds, and umbilical manifolds. The final chapter discusses geometric inequalities of submanifolds, results in Morse theory and their applications, and total mean curvature of a submanifold. Suitable for graduate students and mathematicians in the area of classical and modern differential geometries, the treatment is largely self-contained. Problems sets conclude each chapter, and an extensive bibliography provides background for students wishing to conduct further research in this area. This new edition includes the author's corrections.
Download or read book Lectures on Hermitian Einstein Metrics for Stable Bundles and K hler 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:
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:
Download or read book Supersymmetric Field Theories written by Sergio Cecotti and published by Cambridge University Press. This book was released on 2015-01-08 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adopting an elegant geometrical approach, this advanced pedagogical text describes deep and intuitive methods for understanding the subtle logic of supersymmetry while avoiding lengthy computations. The book describes how complex results and formulae obtained using other approaches can be significantly simplified when translated to a geometric setting. Introductory chapters describe geometric structures in field theory in the general case, while detailed later chapters address specific structures such as parallel tensor fields, G-structures, and isometry groups. The relationship between structures in supergravity and periodic maps of algebraic manifolds, Kodaira-Spencer theory, modularity, and the arithmetic properties of supergravity are also addressed. Relevant geometric concepts are introduced and described in detail, providing a self-contained toolkit of useful techniques, formulae and constructions. Covering all the material necessary for the application of supersymmetric field theories to fundamental physical questions, this is an outstanding resource for graduate students and researchers in theoretical physics.
Download or read book Arbeitstagung Bonn written by Friedrich Hirzebruch and published by Lecture Notes in Mathematics. This book was released on 1985 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Manifolds and Differential Geometry written by Jeffrey M. Lee and published by American Mathematical Society. This book was released on 2022-03-08 with total page 671 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential geometry began as the study of curves and surfaces using the methods of calculus. In time, the notions of curve and surface were generalized along with associated notions such as length, volume, and curvature. At the same time the topic has become closely allied with developments in topology. The basic object is a smooth manifold, to which some extra structure has been attached, such as a Riemannian metric, a symplectic form, a distinguished group of symmetries, or a connection on the tangent bundle. This book is a graduate-level introduction to the tools and structures of modern differential geometry. Included are the topics usually found in a course on differentiable manifolds, such as vector bundles, tensors, differential forms, de Rham cohomology, the Frobenius theorem and basic Lie group theory. The book also contains material on the general theory of connections on vector bundles and an in-depth chapter on semi-Riemannian geometry that covers basic material about Riemannian manifolds and Lorentz manifolds. An unusual feature of the book is the inclusion of an early chapter on the differential geometry of hypersurfaces in Euclidean space. There is also a section that derives the exterior calculus version of Maxwell's equations. The first chapters of the book are suitable for a one-semester course on manifolds. There is more than enough material for a year-long course on manifolds and geometry.
Download or read book Seminar on Differential Geometry AM 102 Volume 102 written by Shing-tung Yau and published by Princeton University Press. This book was released on 2016-03-02 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of papers constitutes a wide-ranging survey of recent developments in differential geometry and its interactions with other fields, especially partial differential equations and mathematical physics. This area of mathematics was the subject of a special program at the Institute for Advanced Study in Princeton during the academic year 1979-1980; the papers in this volume were contributed by the speakers in the sequence of seminars organized by Shing-Tung Yau for this program. Both survey articles and articles presenting new results are included. The articles on differential geometry and partial differential equations include a general survey article by the editor on the relationship of the two fields and more specialized articles on topics including harmonic mappings, isoperimetric and Poincaré inequalities, metrics with specified curvature properties, the Monge-Arnpere equation, L2 harmonic forms and cohomology, manifolds of positive curvature, isometric embedding, and Kraumlhler manifolds and metrics. The articles on differential geometry and mathematical physics cover such topics as renormalization, instantons, gauge fields and the Yang-Mills equation, nonlinear evolution equations, incompleteness of space-times, black holes, and quantum gravity. A feature of special interest is the inclusion of a list of more than one hundred unsolved research problems compiled by the editor with comments and bibliographical information.
