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Introduction to Lorentz Geometry

Introduction to Lorentz Geometry
Author: Ivo Terek Couto
Publisher: CRC Press
Total Pages: 351
Release: 2021-01-05
Genre: Mathematics
ISBN: 1000223345

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Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style without loss of precision or mathematical rigor Solution manual available on www.routledge.com/9780367468644


An Introduction to Lorentz Surfaces

An Introduction to Lorentz Surfaces
Author: Tilla Weinstein
Publisher: Walter de Gruyter
Total Pages: 229
Release: 2011-06-24
Genre: Mathematics
ISBN: 311082163X

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The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)


The Geometry of Minkowski Spacetime

The Geometry of Minkowski Spacetime
Author: Gregory L. Naber
Publisher: Courier Corporation
Total Pages: 276
Release: 2003-01-01
Genre: Mathematics
ISBN: 9780486432359

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This mathematically rigorous treatment examines Zeeman's characterization of the causal automorphisms of Minkowski spacetime and the Penrose theorem concerning the apparent shape of a relativistically moving sphere. Other topics include the construction of a geometric theory of the electromagnetic field; an in-depth introduction to the theory of spinors; and a classification of electromagnetic fields in both tensor and spinor form. Appendixes introduce a topology for Minkowski spacetime and discuss Dirac's famous "Scissors Problem." Appropriate for graduate-level courses, this text presumes only a knowledge of linear algebra and elementary point-set topology. 1992 edition. 43 figures.


Global Lorentzian Geometry

Global Lorentzian Geometry
Author: John K. Beem
Publisher: Routledge
Total Pages: 656
Release: 2017-09-29
Genre: Science
ISBN: 1351444719

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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.


Semi-Riemannian Geometry With Applications to Relativity

Semi-Riemannian Geometry With Applications to Relativity
Author: Barrett O'Neill
Publisher: Academic Press
Total Pages: 483
Release: 1983-07-29
Genre: Mathematics
ISBN: 0080570577

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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.


The Geometry of Spacetime

The Geometry of Spacetime
Author: James J. Callahan
Publisher: Springer Science & Business Media
Total Pages: 474
Release: 2013-03-09
Genre: Science
ISBN: 1475767366

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Hermann Minkowski recast special relativity as essentially a new geometric structure for spacetime. This book looks at the ideas of both Einstein and Minkowski, and then introduces the theory of frames, surfaces and intrinsic geometry, developing the main implications of Einstein's general relativity theory.


The Mathematics of Minkowski Space-Time

The Mathematics of Minkowski Space-Time
Author: Francesco Catoni
Publisher: Springer Science & Business Media
Total Pages: 267
Release: 2008-06-29
Genre: Mathematics
ISBN: 3764386142

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This book arose out of original research on the extension of well-established applications of complex numbers related to Euclidean geometry and to the space-time symmetry of two-dimensional Special Relativity. The system of hyperbolic numbers is extensively studied, and a plain exposition of space-time geometry and trigonometry is given. Commutative hypercomplex systems with four unities are studied and attention is drawn to their interesting properties.


Introduction to Differential Geometry of Space Curves and Surfaces

Introduction to Differential Geometry of Space Curves and Surfaces
Author: Taha Sochi
Publisher: Taha Sochi
Total Pages: 252
Release: 2022-09-14
Genre: Mathematics
ISBN:

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This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.


An Introduction to Riemannian Geometry

An Introduction to Riemannian Geometry
Author: Leonor Godinho
Publisher: Springer
Total Pages: 476
Release: 2014-07-26
Genre: Mathematics
ISBN: 3319086669

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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.


The Geometry of Physics

The Geometry of Physics
Author: Frankel Theodore
Publisher: 清华大学出版社有限公司
Total Pages: 724
Release: 2005
Genre: Geometry, Differential
ISBN: 9787302073512

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