LEADER 05408nam 2200673Ia 450 001 9910825965103321 005 20200520144314.0 010 $a1-281-76876-6 010 $a9786611768768 010 $a0-08-057057-7 035 $a(CKB)1000000000554506 035 $a(EBL)405289 035 $a(OCoLC)476222356 035 $a(SSID)ssj0000244064 035 $a(PQKBManifestationID)11190675 035 $a(PQKBTitleCode)TC0000244064 035 $a(PQKBWorkID)10168748 035 $a(PQKB)10553533 035 $a(MiAaPQ)EBC405289 035 $a(EXLCZ)991000000000554506 100 $a19820804d1983 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSemi-Riemannian geometry $ewith applications to relativity /$fBarrett O'Neill 210 $aNew York $cAcademic Press$d1983 215 $a1 online resource (483 p.) 225 1 $aPure and applied mathematics ;$v103 300 $aDescription based upon print version of record. 311 $a0-12-526740-1 320 $aIncludes bibliographical references and index. 327 $aFront Cover; SEMI-RIEMANNIAN GEOMETRY; Copyright Page; 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; CHAPTER 3. SEMI-RIEMANNIAN MANIFOLDS; Isometries 327 $aThe Levi-Civita ConnectionParallel 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; Totally Umbilic Hypersurfaces; The Normal Connection 327 $aA Congruence TheoremIsometric 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; Energy-Momentum; Collisions; An Accelerating Observer 327 $aCHAPTER 7. CONSTRUCTIONSDeck 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; Semiorthogonal Groups; Some Isometry Groups 327 $aTime-Orientability and Space-OrientabilityLinear 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; Reductive Homogeneous Spaces; Symmetric Spaces 327 $aRiemannian Symmetric Spaces 330 $aThis book is an exposition of semi-Riemannian geometry (also called pseudo-Riemannian geometry)--the study of a smooth manifold furnished with a metric tensor of arbitrary signature. The principal special cases are Riemannian geometry, where the metric is positive definite, and Lorentz geometry. For many years these two geometries have developed almost independently: Riemannian geometry reformulated in coordinate-free fashion and directed toward global problems, Lorentz geometry in classical tensor notation devoted to general relativity. More recently, this divergence has been re 410 0$aPure and applied mathematics (Academic Press) ;$v103. 606 $aGeometry, Riemannian 606 $aManifolds (Mathematics) 606 $aCalculus of tensors 606 $aRelativity (Physics) 615 0$aGeometry, Riemannian. 615 0$aManifolds (Mathematics) 615 0$aCalculus of tensors. 615 0$aRelativity (Physics) 676 $a510 s 676 $a516.3/73 700 $aO'Neill$b Barrett$030394 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910825965103321 996 $aSemi-riemannian geometry$975185 997 $aUNINA