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



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
Semiorthogonal group $O_{\nu}(n)=O(p,q)$, fundamental group      310
Semiorthogonal group $O_{\nu}(n)=O(p,q)$, Lie algebra      235
Semiorthogonal linear operator (matrix)      234—238 243 262
Separation      166
Shape operator      107 119
Shape tensor      100 118—121
Sign of curvature tensor      89
Sign of curve      263
Sign of hypersurface      106
Signature      50
Signature, matrix      234
Simple connectedness      442
Simply connected covering      444
Singularity theorem      401
Singularity theorem, Hawking’s      431—432
Singularity theorem, Penrose’s      436
Smooth Euclidean function      1
Smooth mapping of manifolds      4—5
Smooth overlap      2
Space form      227 243—248
Space form, classification of simply connected      227—228
Space form, positive and negative      244
Space-orientation (Space-orientability, Space-oriented)      237 240—242
Spacelike curve      69
Spacelike submanifold (or Riemannian submanifold)      57 142
Spacelike subspace      141
Spacelike vector      56
Spacetime      163 (see also “Individual spacetimes”)
Special orthogonal group $SO(n)=O^{+}(n)$      452
Special orthogonal group $SO(n)=O^{+}(n)$, compactness and connectedness of      237 309—310
Special orthogonal group $SO(n)=O^{+}(n)$, fundamental group of      310
Special orthogonal group $SO(n)=O^{+}(n)$, Lie algebra of      45
Special relativity      158—184
Special relativity and general relativity      332—333
Special unitary group SU(n)      452
Special unitary group SU(n), Lie algebra of      452
Special unitary group SU(n), simple connectedness of      310
speed of light      161—162
Sphere as smooth manifold      3 20 307
Sphere, geometry of      57 94 101 103—104 105 113 137 228 271 318—319
Star      364 384—385
Static spacetime      360—361 363
Stress-energy tensor      335—337 340
Stress-energy tensor of perfect fluid      337—339
Strong energy condition      341
Submanifold, semi-Riemannian      57 97—125
Submanifold, semi-Riemannian, extremal      299
Submanifold, semi-Riemannian, totally geodesic      104—106 125
Submanifold, semi-Riemannian, totally umbilic      106 108
Submanifold, smooth      15—18
Submanifold, smooth, open      3—4
Submersion, semi-Riemannian      212—213
Submersion, smooth      20—21 32 33
Support      6
surface      3 (see also “Semi-Riemannian surface”)
Surface theory, classical      124
Surface theory, semiclassical      262
Symmetric space      224 231
Symmetric space, Lie construction of      315—317
Symmetric space, Riemannian      319—321
Symplectic group Sp(n)      451 452
Symplectic group Sp(n), topological properties of      309—310
Synchronizable observer field      359
Synge’s formula      265
tan (tangential projection)      98 205 344 369
Tangent bundle      26—27
Tangent space      7
Tangent vector      6—7
Tensor (field)      35
Tensor (field), at point      37
Tensor (field), components of      39
Tensor (field), contravariant      35 37
Tensor (field), covariant      35 37 42—43
Tensor (field), derivation      43 52
Tensor (field), metric equivalence of      83
Tensor (field), multiplication      36
Tensor (field), type      35
Tensor (field), type-changing      81—84 (see also “Contraction”)
Test particle      337
Tidal force (Ricci operator)      216 219 278 299 335 362
Tidal force (Ricci operator), Schwarzschild      385—386 399
Time dilation      171
time function      359
Time, Newtonian      159—160
Time, proper      163
Time-orientation (Time-orientability, Time-oriented)      144—145 194 237 240—242
Time-separation      409—411
Timecone      143
Timelike convergence condition      340
Timelike curve      69
Timelike curve, piecewise smooth      146
Timelike submanifold      142
Timelike subspace      141
Timelike vector      56
Topological hypersurface      413
Topological manifold      413
Topological properties of manifolds      21—23
Torsion tensor      93
Totally geodesic submanifold      104 125
Totally umbilic submanifold      106 116—118
Trace form on matrix Lie algebra      303
Transferred vector field      14
Transvection      231
Trapped subset      435
Trapped surface      435
Twin paradox      173
Two-parameter map      122—123
Umbilic point      105
Unit speed curve      132
Unitary group U(n)      451
Unitary group U(n), compactness and connectedness of      309—310 329
Unitary group U(n), fundamental group of      310
Unitary group U(n), Lie algebra of      452
Units, geometric and conventional      162
VACUUM      337
Variation of arc length      263—288
Variation of curve      215
Variation of E      288—293
Variation, geodesic      216
Variation, vector field (infinitesimal variation)      216
Vector bundle      197
Vector field on curve      65
Vector field on curve, perpendicular      218
Vector field on curve, tangent      218
Vector field on manifold      12
Vector field on mapping      27
Vector field on submanifold      97
Vector field on submanifold, normal      98
Vector field on submanifold, tangent      98
Vector field, $\phi$-related      14
Vector space as manifold      25—26
Velocity      10 171
Velocity, parameter      171
Vertical subspace      205 212
Vertical vector (field)      205 212
Volume element      195
Warped product      204
Warped product, causality in      417—418
Warped product, curvature of      210—211
Warped product, fibers      205
Warped product, geodesics in      207—209
Warped product, leaves      205
Warped product, warping function of      204
Worldline      160 163
1 2 3
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2024
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте