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Semi Riemannian Geometry With Applications To Relativity

Semi Riemannian Geometry With Applications to Relativity PDF
Author: Barrett O'Neill
Publisher: Academic Press
ISBN: 9780080570570
Size: 42.26 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 468
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Semi Riemannian Geometry With Applications To Relativity

by Barrett O'Neill, Semi Riemannian Geometry With Applications To Relativity Books available in PDF, EPUB, Mobi Format. Download Semi Riemannian Geometry With Applications To Relativity books, 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.




Semi Riemannian Geometry With Applications To Relativity

Semi Riemannian Geometry With Applications to Relativity PDF
Author: Barrett O'Neill
Publisher: Academic Press
ISBN: 9780125267403
Size: 60.36 MB
Format: PDF, Kindle
Category : Mathematics
Languages : en
Pages : 468
View: 7505

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Semi Riemannian Geometry With Applications To Relativity

by Barrett O'Neill, Semi Riemannian Geometry With Applications To Relativity Books available in PDF, EPUB, Mobi Format. Download Semi Riemannian Geometry With Applications To Relativity books, 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.




Semi Riemannian Geometry

Semi Riemannian Geometry PDF
Author: Stephen C. Newman
Publisher: John Wiley & Sons
ISBN: 1119517532
Size: 78.43 MB
Format: PDF
Category : Mathematics
Languages : en
Pages : 625
View: 737

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Semi Riemannian Geometry

by Stephen C. Newman, Semi Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Semi Riemannian Geometry books, An introduction to semi-Riemannian geometry as a foundation for general relativity Semi-Riemannian Geometry: The Mathematical Language of General Relativity is an accessible exposition of the mathematics underlying general relativity. The book begins with background on linear and multilinear algebra, general topology, and real analysis. This is followed by material on the classical theory of curves and surfaces, expanded to include both the Lorentz and Euclidean signatures. The remainder of the book is devoted to a discussion of smooth manifolds, smooth manifolds with boundary, smooth manifolds with a connection, semi-Riemannian manifolds, and differential operators, culminating in applications to Maxwell’s equations and the Einstein tensor. Many worked examples and detailed diagrams are provided to aid understanding. This book will appeal especially to physics students wishing to learn more differential geometry than is usually provided in texts on general relativity.




Elementary Differential Geometry Revised 2nd Edition

Elementary Differential Geometry  Revised 2nd Edition PDF
Author: Barrett O'Neill
Publisher: Elsevier
ISBN: 9780080505428
Size: 28.85 MB
Format: PDF, ePub, Docs
Category : Mathematics
Languages : en
Pages : 520
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Elementary Differential Geometry Revised 2nd Edition

by Barrett O'Neill, Elementary Differential Geometry Revised 2nd Edition Books available in PDF, EPUB, Mobi Format. Download Elementary Differential Geometry Revised 2nd Edition books, Written primarily for students who have completed the standard first courses in calculus and linear algebra, Elementary Differential Geometry, Revised 2nd Edition, provides an introduction to the geometry of curves and surfaces. The Second Edition maintained the accessibility of the first, while providing an introduction to the use of computers and expanding discussion on certain topics. Further emphasis was placed on topological properties, properties of geodesics, singularities of vector fields, and the theorems of Bonnet and Hadamard. This revision of the Second Edition provides a thorough update of commands for the symbolic computation programs Mathematica or Maple, as well as additional computer exercises. As with the Second Edition, this material supplements the content but no computer skill is necessary to take full advantage of this comprehensive text. Over 36,000 copies sold worldwide Accessible, practical yet rigorous approach to a complex topic--also suitable for self-study Extensive update of appendices on Mathematica and Maple software packages Thorough streamlining of second edition's numbering system Fuller information on solutions to odd-numbered problems Additional exercises and hints guide students in using the latest computer modeling tools




Riemannian Geometric Statistics In Medical Image Analysis

Riemannian Geometric Statistics in Medical Image Analysis PDF
Author: Xavier Pennec
Publisher: Academic Press
ISBN: 0128147253
Size: 54.41 MB
Format: PDF, ePub
Category : Computers
Languages : en
Pages : 636
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Riemannian Geometric Statistics In Medical Image Analysis

by Xavier Pennec, Riemannian Geometric Statistics In Medical Image Analysis Books available in PDF, EPUB, Mobi Format. Download Riemannian Geometric Statistics In Medical Image Analysis books, Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Content includes: - The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs - Applications of statistics on manifolds and shape spaces in medical image computing - Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science. - A complete reference covering both the foundations and state-of-the-art methods - Edited and authored by leading researchers in the field - Contains theory, examples, applications, and algorithms - Gives an overview of current research challenges and future applications




Global Lorentzian Geometry Second Edition

Global Lorentzian Geometry  Second Edition PDF
Author: John K. Beem
Publisher: CRC Press
ISBN: 9780824793241
Size: 35.98 MB
Format: PDF, ePub, Docs
Category : Science
Languages : en
Pages : 656
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Global Lorentzian Geometry Second Edition

by John K. Beem, Global Lorentzian Geometry Second Edition Books available in PDF, EPUB, Mobi Format. Download Global Lorentzian Geometry Second Edition books, 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.




Recent Developments In Pseudo Riemannian Geometry

Recent Developments in Pseudo Riemannian Geometry PDF
Author: Dmitriĭ Vladimirovich Alekseevskiĭ
Publisher: European Mathematical Society
ISBN: 9783037190517
Size: 61.40 MB
Format: PDF, ePub, Mobi
Category : Mathematics
Languages : en
Pages : 539
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Recent Developments In Pseudo Riemannian Geometry

by Dmitriĭ Vladimirovich Alekseevskiĭ, Recent Developments In Pseudo Riemannian Geometry Books available in PDF, EPUB, Mobi Format. Download Recent Developments In Pseudo Riemannian Geometry books, This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric spaces in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research.