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Semi Riemannian Geometry With Applications to Relativity

Semi Riemannian Geometry With Applications to Relativity Author Barrett O'Neill
ISBN-10 0080570577
Release 1983-07-29
Pages 468
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This book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been reversed as physicists, turning increasingly toward invariant methods, have produced results of compelling mathematical interest.



Glimpses of Soliton Theory

Glimpses of Soliton Theory Author Alex Kasman
ISBN-10 9780821852453
Release 2010
Pages 304
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Solitons are explicit solutions to nonlinear partial differential equations exhibiting particle-like behavior. This is quite surprising, both mathematically and physically. Waves with these properties were once believed to be impossible by leading mathematical physicists, yet they are now not only accepted as a theoretical possibility but are regularly observed in nature and form the basis of modern fiber-optic communication networks. Glimpses of Soliton Theory addresses some of the hidden mathematical connections in soliton theory which have been revealed over the last half-century. It aims to convince the reader that, like the mirrors and hidden pockets used by magicians, the underlying algebro-geometric structure of soliton equations provides an elegant and surprisingly simple explanation of something seemingly miraculous. Assuming only multivariable calculus and linear algebra as prerequisites, this book introduces the reader to the KdV Equation and its multisoliton solutions, elliptic curves and Weierstrass -functions, the algebra of differential operators, Lax Pairs and their use in discovering other soliton equations, wedge products and decomposability, the KP Equation and Sato's theory relating the Bilinear KP Equation to the geometry of Grassmannians. Notable features of the book include: careful selection of topics and detailed explanations to make this advanced subject accessible to any undergraduate math major, numerous worked examples and thought-provoking but not overly-difficult exercises, footnotes and lists of suggested readings to guide the interested reader to more information, and use of the software package Mathematica« to facilitate computation and to animate the solutions under study. This book provides the reader with a unique glimpse of the unity of mathematics and could form the basis for a self-study, one-semester special topics, or "capstone" course.



Curvature in Mathematics and Physics

Curvature in Mathematics and Physics Author Shlomo Sternberg
ISBN-10 9780486292717
Release 2013-04-17
Pages 416
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Expert treatment introduces semi-Riemannian geometry and its principal physical application, Einstein's theory of general relativity, using the Cartan exterior calculus as a principal tool. Prerequisites include linear algebra and advanced calculus. 2012 edition.



The Geometry of Kerr Black Holes

The Geometry of Kerr Black Holes Author Barrett O'Neill
ISBN-10 9780486783116
Release 2014-01-15
Pages 400
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Suitable for advanced undergraduates and graduate students of mathematics as well as for physicists, this unique monograph and self-contained treatment constitutes an introduction to modern techniques in differential geometry. 1995 edition.



An Introduction to Riemannian Geometry

An Introduction to Riemannian Geometry Author Leonor Godinho
ISBN-10 9783319086668
Release 2014-07-26
Pages 467
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Unlike many other texts on differential geometry, this textbook also offers interesting applications to geometric mechanics and general relativity. The first part is a concise and self-contained introduction to the basics of manifolds, differential forms, metrics and curvature. The second part studies applications to mechanics and relativity including the proofs of the Hawking and Penrose singularity theorems. It can be independently used for one-semester courses in either of these subjects. The main ideas are illustrated and further developed by numerous examples and over 300 exercises. Detailed solutions are provided for many of these exercises, making An Introduction to Riemannian Geometry ideal for self-study.



Global Lorentzian Geometry Second Edition

Global Lorentzian Geometry  Second Edition Author John K. Beem
ISBN-10 0824793242
Release 1996-03-08
Pages 656
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Bridging the gap between modern differential geometry and the mathematical physics of general relativity, this text, in its second edition, includes new and expanded material on topics such as the instability of both geodesic completeness and geodesic incompleteness for general space-times, geodesic connectibility, the generic condition, the sectional curvature function in a neighbourhood of degenerate two-plane, and proof of the Lorentzian Splitting Theorem.;Five or more copies may be ordered by college or university stores at a special student price, available on request.



Differential Geometry and Relativity Theory

Differential Geometry and Relativity Theory Author RichardL. Faber
ISBN-10 9781351455145
Release 2017-10-19
Pages 272
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Differentilil Geometry and Relativity Theory: An Introduction approaches relativity asa geometric theory of space and time in which gravity is a manifestation of space-timecurvature, rathe1 than a force. Uniting differential geometry and both special and generalrelativity in a single source, this easy-to-understand text opens the general theory of relativityto mathematics majors having a backgr.ound only in multivariable calculus and linearalgebra.The book offers a broad overview of the physical foundations and mathematical details ofrelativity, and presents concrete physical interpretations of numerous abstract concepts inRiemannian geometry. The work is profusely illustrated with diagrams aiding in the understandingof proofs and explanations. Appendices feature important material on vectoranalysis and hyperbolic functions.Differential Geometry and Relativity Theory: An Introduction serves as the ideal textfor high-level undergraduate couues in mathematics and physics, and includes a solutionsmanual augmenting classroom study. It is an invaluable reference for mathematicians interestedin differential and IUemannian geometry, or the special and general theories ofrelativity



Geometry of Manifolds

Geometry of Manifolds Author Richard L. Bishop
ISBN-10 9780821829233
Release 1964
Pages 273
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First published in 1964, this book served as a text on differential geometry to several generations of graduate students all over the world. The first half of the book (Chapters 1-6) presents basics of the theory of manifolds, vector bundles, differential forms, and Lie groups, with a special emphasis on the theory of linear and affine connections. The second half of the book (Chapters 7-11) is devoted to Riemannian geometry. Following the definition and main properties of Riemannian manifolds, the authors discuss the theory of geodesics, complete Riemannian manifolds, and curvature. Next, they introduce the theory of immersion of manifolds and the second fundamental form. The concluding Chapter 11 contains more complicated results on which much of the research in Riemannian geometry is based: the Morse index theorem, Synge's theorem on closed geodesics, Rauch's comparision theorem, and Bishop's volume-comparision theorem. Clear, concise writing as well as many exercises and examples make this classic an excellent text for a first-year graduate course on differential geometry.



Tensors

Tensors Author Anadi Jiban Das
ISBN-10 9780387694696
Release 2007-10-05
Pages 290
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Here is a modern introduction to the theory of tensor algebra and tensor analysis. It discusses tensor algebra and introduces differential manifold. Coverage also details tensor analysis, differential forms, connection forms, and curvature tensor. In addition, the book investigates Riemannian and pseudo-Riemannian manifolds in great detail. Throughout, examples and problems are furnished from the theory of relativity and continuum mechanics.



Eigenvalues in Riemannian Geometry

Eigenvalues in Riemannian Geometry Author Isaac Chavel
ISBN-10 0080874347
Release 1984-11-07
Pages 362
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The basic goals of the book are: (i) to introduce the subject to those interested in discovering it, (ii) to coherently present a number of basic techniques and results, currently used in the subject, to those working in it, and (iii) to present some of the results that are attractive in their own right, and which lend themselves to a presentation not overburdened with technical machinery.



Pure and Applied Mathematics

Pure and Applied Mathematics Author Barrett O'Neill
ISBN-10 0125267401
Release 1983
Pages 468
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Pure and Applied Mathematics has been writing in one form or another for most of life. You can find so many inspiration from Pure and Applied Mathematics also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Pure and Applied Mathematics book for free.



Manifolds and Differential Geometry

Manifolds and Differential Geometry Author Jeffrey Marc Lee
ISBN-10 9780821848159
Release 2009
Pages 671
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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 hyper-surfaces 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.



Relativity

Relativity Author Wolfgang Rindler
ISBN-10 9780198567318
Release 2006-04-06
Pages 430
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This text brings the challenge and excitement of modern relativity and cosmology at rigorous mathematical level within reach of advanced undergraduates and beginning graduates.



Tensor Calculus

Tensor Calculus Author J. L. Synge
ISBN-10 9780486141398
Release 2012-04-26
Pages 336
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Fundamental introduction of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. Topics include spaces and tensors; basic operations in Riemannian space, curvature of space, more.



Global Lorentzian geometry

Global Lorentzian geometry Author John K. Beem
ISBN-10 STANFORD:36105031983187
Release 1981
Pages 460
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Global Lorentzian geometry has been writing in one form or another for most of life. You can find so many inspiration from Global Lorentzian geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Global Lorentzian geometry book for free.



Elementary Differential Geometry

Elementary Differential Geometry Author Barrett O'Neill
ISBN-10 9781483268118
Release 2014-05-12
Pages 422
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Elementary Differential Geometry focuses on the elementary account of the geometry of curves and surfaces. The book first offers information on calculus on Euclidean space and frame fields. Topics include structural equations, connection forms, frame fields, covariant derivatives, Frenet formulas, curves, mappings, tangent vectors, and differential forms. The publication then examines Euclidean geometry and calculus on a surface. Discussions focus on topological properties of surfaces, differential forms on a surface, integration of forms, differentiable functions and tangent vectors, congruence of curves, derivative map of an isometry, and Euclidean geometry. The manuscript takes a look at shape operators, geometry of surfaces in E, and Riemannian geometry. Concerns include geometric surfaces, covariant derivative, curvature and conjugate points, Gauss-Bonnet theorem, fundamental equations, global theorems, isometries and local isometries, orthogonal coordinates, and integration and orientation. The text is a valuable reference for students interested in elementary differential geometry.



Tensors Differential Forms and Variational Principles

Tensors  Differential Forms  and Variational Principles Author David Lovelock
ISBN-10 9780486131986
Release 2012-04-20
Pages 400
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Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.