Book description
An introduction to semiRiemannian geometry as a foundation for general relativity
SemiRiemannian 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, semiRiemannian 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.
STEPHEN C. NEWMAN is Professor Emeritus at the University of Alberta, Edmonton, Alberta, Canada. He is the author of Biostatistical Methods in Epidemiology and A Classical Introduction to Galois Theory, both published by Wiley.
Table of contents
 Cover
 Preface

Part I: Preliminaries
 Chapter 1: Vector Spaces
 Chapter 2: Matrices and Determinants
 Chapter 3: Bilinear Functions
 Chapter 4: Scalar Product Spaces
 Chapter 5: Tensors on Vector Spaces
 Chapter 6: Tensors on Scalar Product Spaces
 Chapter 7: Multicovectors
 Chapter 8: Orientation
 Chapter 9: Topology
 Chapter 10: Analysis in ℝ m

Part II: Curves and Regular Surfaces
 Chapter 11: Curves and Regular Surfaces in ℝ3

Chapter 12: Curves and Regular Surfaces in
 12.1 Curves in
 12.2 Regular Surfaces in
 12.3 Induced Euclidean Derivative in
 12.4 Covariant Derivative on Regular Surfaces in
 12.5 Covariant Derivative on Curves in
 12.6 Lie Bracket in
 12.7 Orientation in
 12.8 Gauss Curvature in
 12.9 Riemann Curvature Tensor in
 12.10 Computations for Regular Surfaces in
 Chapter 13: Examples of Regular Surfaces

Part III: Smooth Manifolds and Semi‐Riemannian Manifolds
 Chapter 14: Smooth Manifolds

Chapter 15: Fields on Smooth Manifolds
 15.1 Vector Fields
 15.2 Representation of Vector Fields
 15.3 Lie Bracket
 15.4 Covector Fields
 15.5 Representation of Covector Fields
 15.6 Tensor Fields
 15.7 Representation of Tensor Fields
 15.8 Differential Forms
 15.9 Pushforward and Pullback of Functions
 15.10 Pushforward and Pullback of Vector Fields
 15.11 Pullback of Covector Fields
 15.12 Pullback of Covariant Tensor Fields
 15.13 Pullback of Differential Forms
 15.14 Contraction of Tensor Fields
 Chapter 16: Differentiation and Integration on Smooth Manifolds
 Chapter 17: Smooth Manifolds with Boundary
 Chapter 18: Smooth Manifolds with a Connection

Chapter 19: Semi‐Riemannian Manifolds
 19.1 Semi‐Riemannian Manifolds
 19.2 Curves
 19.3 Fundamental Theorem of Semi‐Riemannian Manifolds
 19.4 Flat Maps and Sharp Maps
 19.5 Representation of Tensor Fields
 19.6 Contraction of Tensor Fields
 19.7 Isometries
 19.8 Riemann Curvature Tensor
 19.9 Geodesics
 19.10 Volume Forms
 19.11 orientation of Hypersurfaces
 19.12 Induced Connections
 Chapter 20: Differential Operators on Semi‐Riemannian Manifolds
 Chapter 21: Riemannian Manifolds
 Chapter 22: Applications to Physics
 Part IV: Appendices
 Further Reading
 Index
 End User License Agreement
Product information
 Title: SemiRiemannian Geometry
 Author(s):
 Release date: July 2019
 Publisher(s): Wiley
 ISBN: 9781119517535
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