عنوان
پدید آورنده
موضوع
رده
QA649 -- O645 1983eb
QA649
--
O645
1983eb
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
0080570577
(Number (ISBN
9780080570570
NATIONAL BIBLIOGRAPHY NUMBER
Number
b734006
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Semi-Riemannian Geometry With Applications to Relativity, 103.
General Material Designation
[Book]
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
Burlington :
Name of Publisher, Distributor, etc.
Elsevier Science,
Date of Publication, Distribution, etc.
2014.
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource (483 pages).
SERIES
Series Title
Pure and Applied Mathematics ;
Volume Designation
v. 103
GENERAL NOTES
Text of Note
Reductive Homogeneous Spaces.
CONTENTS NOTE
Text of Note
Front Cover; Semi-Riemannian Geometry: With Applications to Relativity; Copyright Page; Table of Contents; Preface; Notation and Terminology; CHAPTER 1. MANIFOLD THEORY; Smooth Manifolds; Smooth Mappings; Tangent Vectors; Differential Maps; Curves; Vector Fields; One-Forms; Submanifolds; Immersions and Submersions; Topology of Manifolds; Some Special Manifolds; Integral Curves; CHAPTER 2. TENSORS; Basic Algebra; Tensor Fields; Interpretations; Tensors at a Point; Tensor Components; Contraction; Covariant Tensors; Tensor Derivations; Symmetric Bilinear Forms; Scalar Products.
Text of Note
CHAPTER 3. SEMI-RIEMANNIAN MANIFOLDSIsometries; The Levi-Civita Connection; Parallel Translation; Geodesics; The Exponential Map; Curvature; Sectional Curvature; Semi-Riemannian Surfaces; Type-Changing and Metric Contraction; Frame Fields; Some Differential Operators; Ricci and Scalar Curvature; Semi-Riemannian Product Manifolds; Local Isometries; Levels of Structure; CHAPTER 4. SEMI-RIEMANNIAN SUBMANIFOLDS; Tangents and Normals; The Induced Connection; Geodesics in Submanifolds; Totally Geodesic Submanifolds; Semi-Riemannian Hypersurfaces; Hyperquadrics; The Codazzi Equation.
Text of Note
Energy-MomentumCollisions; An Accelerating Observer; CHAPTER 7. CONSTRUCTIONS; Deck Transformations; Orbit Manifolds; Orientability; Semi-Riemannian Coverings; Lorentz Time-Orientability; Volume Elements; Vector Bundles; Local Isometries; Matched Coverings; Warped Products; Warped Product Geodesics; Curvature of Warped Products; Semi-Riemannian Submersions; CHAPTER 8. SYMMETRY AND CONSTANT CURVATURE; Jacobi Fields; Tidal Forces; Locally Symmetric Manifolds; Isometries of Normal Neighborhoods; Symmetric Spaces; Simply Connected Space Forms; Transvections; CHAPTER 9. ISOMETRIES.
Text of Note
Semiorthogonal GroupsSome Isometry Groups; Time-Orientability and Space-Orientability; Linear Algebra; Space Forms; Killing Vector Fields; The Lie Algebra i(M); I(M) as Lie Group; Homogeneous Spaces; CHAPTER 10. CALCULUS OF VARIATIONS; First Variation; Second Variation; The Index Form; Conjugate Points; Local Minima and Maxima; Some Global Consequences; The Endmanifold Case; Focal Points; Applications; Variation of E; Focal Points along Null Geodesics; A Causality Theorem; CHAPTER 11. HOMOGENEOUS AND SYMMETRIC SPACES; More about Lie Groups; Bi-Invariant Metrics; Coset Manifolds.
Text of Note
Totally Umbilic HypersurfacesThe Normal Connection; A Congruence Theorem; Isometric Immersions; Two-Parameter Maps; CHAPTER 5. RIEMANNIAN AND LORENTZ GEOMETRY; The Gauss Lemma; Convex Open Sets; Arc Length; Riemannian Distance; Riemannian Completeness; Lorentz Causal Character; Timecones; Local Lorentz Geometry; Geodesics in Hyperquadrics; Geodesics in Surfaces; Completeness and Extendibility; CHAPTER 6. SPECIAL RELATIVITY; Newtonian Space and Time; Newtonian Space-Time; Minkowski Spacetime; Minkowski Geometry; Particles Observed; Some Relativistic Effects; Lorentz-Fitzgerald Contraction.
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SUMMARY OR ABSTRACT
Text of Note
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 re.
OTHER EDITION IN ANOTHER MEDIUM
Title
Semi-Riemannian Geometry With Applications to Relativity, 103.
International Standard Book Number
9780125267403
TOPICAL NAME USED AS SUBJECT
Calculus of tensors.
Geometry, Riemannian.
Manifolds (Mathematics)
Relativity (Physics)
DEWEY DECIMAL CLASSIFICATION
Number
510
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA649
--
O645
1983eb
PERSONAL NAME - PRIMARY RESPONSIBILITY
O'Neill, Barrett.
ORIGINATING SOURCE
Date of Transaction
20201216055649.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
