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Besse A.L. — Einstein Manifolds
Besse A.L. — Einstein Manifolds



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Название: Einstein Manifolds

Автор: Besse A.L.

Аннотация:

Einstein's equations stem from General Relativity. In the context of Riemannian manifolds, an independent mathematical theory has developed around them. Recently, it has produced several striking results, which have been of great interest also to physicists. This Ergebnisse volume is the first book which presents an up-to-date overview of the state of the art in this field. "Einstein Manifold"s is a successful attempt to organize the abundant literature, with emphasis on examples. Parts of it can be used separately as introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 516

Добавлена в каталог: 19.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Lorentz manifold      309 310 425
Lorentz metric      29
Lorentz symmetric space      206
Mass/energy      96
Maximum principle      173 327 328 430 466
Mean curvature vector      38 243
Minimal submanifold      38
Minkowski space      205
Moduli Space of Einstein Structures      9 340 352 361 365 471 475
Moment map      380 477
Monge — Ampere equation      327 424 429
monodromy      288
Motion      178
Musical isomorphism      30
Myers theorem      146 149 165
Nash — Moser implicit function theorem      147
Natural Lagrangian      118
Naturally reductive      193 196 450
Nearly effectively      179 180
Negative curvature (compact space of)      354
Negative curvature (constant)      155 158
Newlander — Nirenberg theorem      68 381 414
Nijenhuis tensor      67
Noncharacteristic directions      142
Normal coordinates      32 143 144 145
Normal homogeneous metric      197 210 221 374
Null curve      95
Obstruction space      349 351
One parameter subgroup      181 193
Orbifold      346 361
Orbit      208
Oriented cobordism ring      171
Orthogonal group      180
Overdetermined      462 463
O’Neill tensors      238
Page metric      273 337 338
Pair of pants      156
Palais — Smale condition      151 373
parallel      25
Parallel translation      280
Partial alternation (on 3-tensors)      434
Partial symmetrization (on 3-tensors)      434
Past (see your own)      107
Path      244
Penrose construction      379
Perihelion procession      107
Period mapping on complex structures      367
Period mapping on Einstein structures      366
Period mapping on Kahler — Einstein structures      367
Photon sphere      106
Pinched sectional curvature      357
Planetary orbits      105 107
Plurisubharmonic (strictly)      423
Poincare’s conjecture      147
Poisson bracket      330
Pontryagin class      370
Pontryagin number      6
Positive (negative) spin bundle      372 380
Positive 2-form      70
Positive cohomology class      319
Positive spin bundle      169 346 352
Premoduli space of Einstein Structures      361
Prime      157
Primitive form      71
Primitive part of a form      71 334
Primitive roots      225
Principal connection      248
Principal orbit      237
Principal pressure      96
Principal symbol      169
PRODUCT      29 44
Projectable (vector field)      210 239
Projective algebraic manifold      322
Pseudo-Anosov      158
Pseudo-Riemannian immersion      37
Pseudo-Riemannian metric      29
Pseudoconvex (strictly)      428
Pseudosphere      145
Pure curvature operator      439
Pure Weyl tensor      439
Quadratic functional      133 333 337
Quasilinear      459
Quaternion-Hermitian manifold      410
Quaternion-Kahler manifold      285 307 396 403
Quaternion-Kahler symmetric spaces (table of)      409
Quaternionic manifold      411
Rank      298 299
Ray      37 172
Reducible Kahler manifold      288
Reducible Riemannian manifold      285
Reductive      331
Regular      211
Restricted holonomy group      280 287 294
Reverse Penrose construction      385
Ricci contraction      46
Ricci curvature      2 15 42
Ricci equation      38
Ricci flat      124 128 135 191 209
Ricci form      73 216 218 284 319 428
Ricci formula      26
Ricci potential      90
Ricci symbol      452
Riemann domain      429
Riemann — Roch — Hirzebruch theorem      86 365 367
Riemannian metric      1 29
Riemannian product      285
Riemannian structure      1
Riemannian structures (spaces of)      341
Riemannian submersion      236
Rigid      355
Roots (complementary)      218
Roots (positive)      212
Roots (primitive)      225
Rough Laplacian      52
Saturated holonomy system      304
Scalar curvature      15 43 185 319
Schauder estimate      463
Schwarzschild metric      106 113 425
Schwarzschild model      106 113 425
Second fundamental form      38 60
Sectional curvature      42
Self-dual connection (anti)      369 372
Self-dual form      370
Self-dual part of Weyl tensor      50
Semi-simple      195 198 199 331
Serre duality      84
Sharp      30
Signature      140 142 145 161 256 325 366 371
Signature theorem (Hirzebruch)      161 370
SIMPLE      195 199 201 202
Simple components      209
Simplicial volume      164
Simply transitively      178 180 190
Slice      116 341 345
Smooth function      21
Sobolev class      457
Sobolev inequality      120 146 151 458
Space of Kahler — Einstein structures      365 368
Space of Riemannian structures      341
Space-like curve      95
Spacetime singularities      115
Spectrum of the Laplacian      128 130 347
speed of light      94
Sphere      29 128 130 132 354 355
Spheres (groups acting transitively on)      179 300
Spin      169
Spin, bundle (positive)      169 373 380
Spin, cobordism ring      170
Standard homogeneous metric      198
Stein manifold      431
Stress tensor      96
Stress/energy tensor      96
Strongly elliptic      465
Strongly isotropy irreducible space      187
Structural group (of a fibre bundle)      246
Subharmonic      174
Support function      172
Symbol      460
Symmetric infinitesimal complex deformation      363
Symmetric Lorentz space      206
Symmetric space      186 294
Symmetric spaces (compact hermitian)      224
Symmetric spaces (tables of compact irreducible)      201 312 313 314 317
Symmetric spaces (tables of non-compact irreducible)      202 315 316 317
Symmetric spaces (tables of quaternion-Kahler)      409
Symplectic structure      220 383 477
Symplectic structure (complex)      398
Tangent bundle      21
Taub-NUT metric      104 369 395 480
Tautological section      211
Teichmiiller space of Einstein structures      340 343 365 367
Test particle      95
Tidal stress      97
Timelike curve      95
Torsion      26 279
Torus      180 191 226 281 286 287
Torus (complex)      76
Total scalar curvature      4 116 119 128 346 352
Totally geodesic      38 285 286 288
Totally geodesic fibers (submersion with)      235 240 249
Trace      71 72
Transgression      222 223
Transitive action      178
Translations (group of)      178
Travel time of light      109 110
Trivial connection      23
Twisted Dirac Laplacian      56
Twisted Dirac operator      56
Twistor space      380
Twistor space (quaternionic style)      397 412
Two-point homogeneous spaces      186
Type of a form      67
Type of a vector      67
Types (of irreducible symmetric spaces)      195
Umbilic point      38 437
Underdetermined      462 463
Unimodular      184 190
Universal covering      165 191 193 205 323
Vacuum space time      96
Vector field      21
Vector field (basic)      240
Vector field (fundamental)      209
Vector field (hamiltonian)      330
Vector field(holomorphic)      87 329 330 332 334
Vector field(Killing)      334 346
Vertical      236
Very ample      323
Vilms theorem      249
Volume      319 353
Volume element      32
Volume form      33
Volume form (complex)      215 284
Wang theorem      265
Warped product      237
Weak solution      460
Weight      212 217
Weingarten equation      38
Weitzenbock formula      53 74 166 169 178 341 362 376 399 436 448
Weyl chamber      227
Weyl curvature tensor      337
Weyl group      227
Weyl tensor      48 60 78 370
Weyl tensor (harmonic)      434 443
Weyl tensor (self-dual part of)      50 337 370 451
Weyl — Schouten tensor      62
Yamabe invariant      122
Yang — Mills      136 243 371 444
Young symmetrizer      46
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