Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
O'Neill B. — Semi-Riemannian Geometry: With Applications to Relativity
O'Neill B. — Semi-Riemannian Geometry: With Applications to Relativity

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Semi-Riemannian Geometry: With Applications to Relativity

Автор: O'Neill B.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 1983

Количество страниц: 468

Добавлена в каталог: 04.07.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$E=mc^{2}$      177
$\epsilon$-neighborhood      134
$\phi$-related vector fields      14
Acausal set      415
Acceleration      66 159
Achronal set      413
Action of group      254
Action of group, transitive      255
Ad(H)-invariance      301
Age of universe      352—353 362
Angular momentum, Newtonian      453
Angular momentum, Schwarzschild      373—374 380
Anti-isometry      92
Arc length      131
Arc length, first variation of      263 264
Arc length, local maximum and minimum of      272—276
Arc length, second variation of      266
Associated Newtonian particle      168
At rest in Newtonian space      161
At rest in Schwarzschild exterior      372
Atlas      2
Automorphism of Lie algebra      302
Automorphism of Lie group      300
Backwards Schwarz inequality      144
Backwards triangle inequality      144
Basis Theorem      8
Beem and Buseman’s example      209
Bending of light      381
Bi-invariant metric      304—306 330
Bianchi identity, first      75
Bianchi identity, second      76
big bang      348
Big crunch      348
Bilinear form, symmetric      46 53
Black hole      367 392—394
Black hole, formation of      385
Black hole, no escape from      392
Bochner’s theorem      259
Boost      236
Bracket operation in Lie algebra      447
Bracket operation on vector fields      13 31
Bump function      6
Canonical isomorphisms      26
Cartan, E.      224
Cauchy development      419—423
Cauchy horizon      428—431
Cauchy hypersurface      415—417 431
Cauchy hypersurface, future      438
Causal (nonspacelike) curve      146
Causal character of curve      69
Causal character of submanifold      142
Causal character of vector      56
Causal character of vector subspace      141
Causal cone      146 155
Causal future [past], $J^{+}$ $[J^{-}]$      402
Causality conditions      407
Causality in Lorentz manifolds      293—298 401—437
Causality in Special Relativity      165—166
Causality relations      402
Chain rule      10
Christoffel symbols      62
Chronological future [past], $I^{+}$ $[I^{-}]$      402
Chronology condition      407
Clifton — Pohl torus      193 260
Closed geodesic      192
Closed subgroup      447
Codazzi equation      115
Codimension      20 98
Collision      179—181
Complete atlas      2 33
Complete semi-Riemannian manifold      see “Geodesic completeness”
Complete vector field      29
Complete, metrically      138
Complex Grassmann manifold      326 327
Complex hyperbolic space      327
Complex projective space      327—329
Complex structure J on a vector space      324
Component, connected      21
Components of tensor      39 52
Conformal mapping      92
Congruence      102 120
Conjugate point      270—273
Conjugate point on cospacelike geodesics      274—277 299
Conjugate point on null geodesics      see “Focal points”
Connectedness      21 72
Connectedness, geodesic      138
Connection      59
Connection, Levi-Civita      61
Connection, natural, on $R^{n}_{\nu}$      59 62
Connection, normal      118
Conservation lemma      252
Conservation of energy-momentum      179—181
Conservation of energy-momentum, infinitesimal      335
Conservation of Newtonian energy and momentum      453—454
Constant curvature      79—80
Constant curvature, manifolds of      113 223 227—231
Contraction of tensor, metric      83
Contraction of tensor, natural      40—42
Contravariant tensor      37
Convergence k      287—288 292 431—435
Convex open covering      131
Convex open set      129
Coordinate expression      4 5
Coordinate function      2
Coordinate neighborhood      3
Coordinate system      1—3
Coordinates, adapted to subset      16
Coordinates, associated Lorentz      167
Coordinates, cylindrical, on $R^{3}$      63
Coordinates, Euclidean      159
Coordinates, Kruskal-spherical      390
Coordinates, Lorentz (or inertial)      164
Coordinates, natural, on $R^{n}$      1
Coordinates, normal      72—73
Coordinates, null      153 156
Coordinates, Schwarzschild      152
Coordinates, Schwarzschild-spherical      370
Coordinates, spherical, on $R^{3}$      94—95
Coset manifold      306—309
Cosmological model      341
Cospacelike geodesic      273
Cotangent space      14
Covariant derivative      59 64
Covariant derivative of vector field on curve      65
Covariant derivative, normal      114 119
Covariant differential      64
Covariant tensor      37
Covering by subsets      21
Covering by subsets, open      21
Covering, manifold      444
Covering, map      443
Covering, semi-Riemannian      191 201—202
Critical point      33
Critical point of E      290
Critical point of length function      268
Cross section (or section)      xiii
Cross section (or section), local      32
Curl      95
Curvature and gravity      334
Curvature operator      74
Curvature tensor, Riemannian (or Riemann — Christoffel)      74 96
Curvature tensor, Riemannian (or Riemann — Christoffel), components of      76 83
Curvature tensor, Riemannian (or Riemann — Christoffel), normal      125
Curvature tensor, Riemannian (or Riemann — Christoffel), sign of      89
Curvature tensor, Riemannian (or Riemann — Christoffel), symmetries of      75
Curvature, Gauss — Kronecker      197
Curvature, Gaussian      81
Curvature, holomorphic      325
Curvature, mean      see “Mean curvature”
Curvature, normal      see “Normal curvature vector”
Curvature, Ricci      87—89
Curvature, Riemannian      see “Curvature tensor”
Curvature, scalar      88
Curvature, sectional      77—79
Curvaturelike function      79
Curve      10
Curve segment      11
Curve, causal (nonspacelike)      146
Curve, null      69
Curve, parameter      122
Curve, periodic      29
Curve, piecewise smooth      11
Curve, regular      11
Curve, spaceUke      69
Curve, timelike      69
Dajczer and Nomizu’s criteria      53
de Sitter spacetime      229
Deck transformation      185
Derivation      12
Diameter of Riemannian manifold      279
Diffeomorphism      55
Differential form      43
Differential map      9
Differential of function      15 33
Dimension of manifold      3
Direct product and direct sum      34
Displacement vector      131 165
Distance in Robertson — Walker cosmology      347
Distance in special relativity      166 171
Distance, Riemannian      134 136—138
Distant paralleUsm      67
Divergence      195 213
Dot product      1 47
Duality of symmetric spaces      321—323
Dust      see “Friedmann cosmological models”
Edge of achronal set      413
Einstein addition law      172
Einstein equation      336
Einstein gravitational tensor      336
Einstein manifold      96
Einstein — de Sitter model      352 356 357
Einstein, A.      54 172 173 177 332 334 336
Endpoint of extendible curve      30
Energy, density of perfect fluid      339
Energy, Newtonian      159 177
Energy, relativistic      177—180 333
Energy, Schwarzschild      374
Energy-momentum as source of gravity      335
Energy-momentum of lightlike particle      178 333
Energy-momentum of material particle      176 333
Energy-momentum, conservation of      179—180
Euclidean space      1 3 55 228
Evelyn and Jean      183
Evenly covered      443
Event      160 163 333
Event horizon      438
Expansion of universe      347—348
Exponential map      70—71
Exponential map, examples of      73 104
Exponential map, Lie      449—450
Exponential map, normal      199
Extendible curve      30 438
Extendible geodesic      68 130
Extendible manifold      155 157
Extrinsic geometry      102
Fiber of vector bundle      197
Fiber of warped product      204 205
First variation of arc length      263—265
First variation of E      289
Fixed endpoint homotopy      441
Flat manifold      79
Flow      29
Focal point      283—284
Focal point on cospacelike geodesics      285—288
Focal point on null geodesics      290—293 296 298
force      159
Frame (orthonormal)      84
Frame field      84—85
Frame-homogeneous manifold      258—259 260
Free fall      164 334
Friedmann cosmological models      350—353 356—357 362
Fundamental group      442
future      163
Future Cauchy hypersurface      438
Future cone (causal, null, timelike)      163
Future-convergence      435 436
Future-pointing curve      163
Future-pointing vector      163
G-invariant metric      310
G-orientation      241
Galaxies      341
Galaxies, idealizations of      341—342
Gauss equation      100 101 107
Gauss lemma      126—127
Gauss map      196
Gauss, K.F.      54 74
Gaussian curvature      81 124
General (or full) linear group GL(n,R)      446
General (or full) linear group GL(n,R), complex      449
General relativity, foundations of      332—337
Geodesic      67
Geodesic completeness      68
Geodesic completeness from point      138
Geodesic completeness, null      154
Geodesic completeness, spacelike      154
Geodesic completeness, timelike      154
Geodesic symmetry      223
Geodesic, broken      72
Geodesic, causal character of      69
Geodesic, closed      192—193
Geodesic, inextendible (maximal)      68
Geodesic, minimizing (shortest), maximizing (longest)      136—138 156 409 411
Geodesic, minimizing (shortest), maximizing (longest), locally      272 276
Geodesics in cylinders      148
Geodesics in hyperquadrics      149—150
Geodesics in submanifolds      102—103
Geodesics in surfaces      150—153
Geodesics, local properties of      133—135 147—148
Geodesics, variational properties of      263—299
Geometric units      162
Geroch, R.P.      423
Geroch’s example      154
Global hyperbolicity      412
Global symmetry      224 231
Gradient      85
Grassmann manifold, complex      326 327
Grassmann manifold, real      308 310
Hadamard’s Theorem      278
Hawking, S.W.      401
Hawking’s singularity theorem      431—434
Hermitian scalar product      324
Hessian and index form      268—269 290
Hessian of function      33 86
Holomorphic curvature      325
Homogeneous space      257
Homogeneous space, naturally reductive      312
Homogeneous space, normal      330
Homogeneous space, reductive      310
Homomorphism of fundamental groups      443
Homomorphism of Lie algebras      448
Homomorphism of Lie groups      329
Homothety      92
Homotopy, fixed endpoint      441
Hopf — Rinow theorem      138
Hopf’s corollary      228
Horizontal, subspace      205—212
Horizontal, vector (field)      205 212
Hubble law      347
Hubble time      348
Hyperbolic angle      144 156
1 2 3
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте