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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
$dd^c$-Lemma      326
$L^p$ estimate      463
$\hat{A}$-genus      170
3-momentum      95
4-velocity      95
Absolutely simple      195 202
Adjoint      460
Adjoint, representation      182 188 194 199 208 297
Affine connection      278
Albanese torus      320
Algebraic curvature tensor      46
Almost complex structure      66 284
Almost complex structure, Kahler structure      255
Almost complex structure, quaternionic manifold      410
Ambrose — Singer Theorem      291
Amenable      158
ample      322
Anti-canonical line bundle      82 320
Anti-self-dual connection      369 372
Apte formula      80
Associated 2-form      70
Associated 2-form connection      248
Aubin — Calabi — Yau metric      323
Aubin — Calabi — Yau metric theorem      323
Automorphism group      86 320 322 329 331 368
Bach tensor      135
Basic vector field      240
Bending of light      109
Berger — Simons theorem      300
Bergmann manifold      424
Bergmann manifold, metric      77 320
Betti number      161 166 167 302 306 323
Bian(g, r)      138
Bianchi identity      27 41 120 138 286 293 294 300 348 434
Bianchi identity, map      46
Bishop’s theorem      16
Black hole      112
Blowing up      321 331 334 338
Bochner method      53 166 324 399 466
Bochner method, theorem      233 57 166 378
Borel — Lichnerowicz theorem      290
Busemann function      172
Calabi Conjecture      83 322
Calabi — Eckmann manifold      84
Calabi — Yau metric      323
Canonical line bundle      82 284 320 365 401
Canonical line bundle, sheaf      400
Canonical line bundle, variation (of a Riemannian submersion)      252
Capture of light      109 110
Cartan subalgebra      298 409
Cartan — Janet theorem      145
Cartan — Kahler Theorem      302
Casimir operator      197 376
Causal geodesic      108
Cayley numbers      298
Cheeger — Gromoll Theorem      171 308 323
Chern class      78 302 320 326 371
Chern connection      82
Chern number      321 392
Chern — Weil homomorphism      78
Christoffel symbol      23 30 144
Clifford algebra      169
Closed trapped surface      115
Codazzi equation      434
Codazzi tensor      434
Codazzi — Mainardi equation      38
Codifferential      34
Cohomogeneity      275 471 472 475
Complementary roots      218
complete      36
Complete (Ehresmann-)      244
Complete intersection      320
Complete orbit      209
Complex connection      25
Complex dimension      66
Complex exterior derivative      68
Complex exterior derivative of vector-valued form      69
Complex Laplacian      54
Complex manifold      68
Complex projective space      76
Complex symplectic structure      365 398 402
Complex torus      76
Complex volume form      215 284
conformal      121 122 337
Conformal change of metric      58
Conformally flat      60 122 136
Conformally flat (half)      135 136 372 380
Conjugate point      28
Connected sum      157 161 163 164 171
Connection      22
Connection, (anti self-dual)      369 372
Connection, (associated)      248
Connection, (Ehresmann-)      244
Connection, (G-)      247
Connection, (G/(F)-)      247
Connection, (Levi — Civita)      30
Connection, (principal)      248
Contraction (on 3-tensors)      434
Contraction by Kahler form      71
Cosmological constant      96
Cotangent bundle      21
Covariant derivative      22 25 282
Critical      116 119 121 132 134 135
Curvature      24
Curvature, acting on exterior 2-forms      51
Curvature, acting on symmetric 2-tensors      51
Curvature, endomorphism      153 290 291 296 303
Curvature, tensor      30 41
Curvature, tensor (algebraic)      46
de Rham’s holonomy theorem      240 288
Decomposition of Kahler curvature      77
Dehn surgery      159
Del Pezzo surfaces      321
Diameter      36 165 359
Diffeomorphism group      116 117 340
Differential form      21
Dirac Laplacian      54
Dirac Laplacian, operator      55 369 375
Direct sum of connections      24
Distance      36
Distance, spheres      257 258
Divergence      125 35
Divergence form (in)      459
Divisor      367
Dolbeault complex      350
Dolbeault theorem      84 350
Domain of holomorphy      423 429
D’Atri spaces      450 451
Effective divisor      367
Ehresmann connection      244
Ehresmann theorem      244
Eigenspace distribution      436
Eigenvalue function      436
Einstein equation      96 104 113
Einstein equation (linearized)      346
Einstein manifold      3
Einstein operator      346
Einstein structure      340
Elie Cartan theorem      295
Elliptic (overdetermined)      462 463
Elliptic (strongly)      465
Elliptic (underdetermined)      462 463
Elliptic complex      375 462
Elliptic operator      123 327 462
Enriques surface      162 400
Euclidean connection      25
Euler characteristic      161 325 371 400
Euler number (of complex manifold)      86
Euler — Lagrange equation      122
Exceptional divisor      321
Exponential map      28
Exterior derivative (complex)      68
Exterior differential      21
Exterior differential of a vector valued form      24 434
Extremal metric      333
Faithful      178
Fat bundle      242
Finsler metric      1
First Chern class      320
First variation      62
Flag manifold      211
Flat      30
Flat manifold      345
Formal series      349 352
Formally integrable      349 352 361
Fredholm alternative      464
Frohlicher spectral sequence      84
Fubini — Study metric      256
Functional (Riemannian)      118 119
Fundamental class in homology      164
Fundamental group      157 164 167 171 177 189
Fundamental principle of holonomy      282
Fundamental vector field      209
Futaki functional      92 332 375 475
G-connection      247
G/(F)-connection      247
Gauss curvature      49
Gauss equation      38 102
Gauss lemma      32
Gauss — Bonnet      161 371
Geodesic      27 36
Geodesic normal coordinates      32 143 144 145
Geodesic symmetry      191 295 296
Geodesies (first integrals)      108
Geodesies, (Lorentz incomplete)      112 113
Gradient      34 119
Gravitational potential      96
Growth function      167
Haken      159
Half conformally flat      135 136 372
Hamiltonian vector field      330 477
Harmonic coordinates      143
Harmonic curvature      434
Harmonic map      243
Harmonic Weyl tensor      434
Hermann theorem      245 249
Hermitian (infinitesimal Einstein deformation)      362 363
Hermitian, connection      25
Hermitian, metric      69
Hermitian, symmetric spaces (compact)      224
hessian      34
Hirzebruch surfaces      321
Hodge *-operator      33 49 99 369 341
Hodge index formula      366
Holder spaces      143 327 429 456
Holomorphic line bundle      81
Holomorphic sectional curvature      75
Holomorphic vector field      87 329 330 332 334
Holomorphy potential      88
Holonomy group      280
Holonomy representation      280
Homogeneous Kahler manifold (compact)      208 224
Homogeneous Kahler manifold (non-compact)      431
Homogeneous Lorentz manifold      205
Homotopically atoroidal      157
Hopf bundle      332 335 383
Hopf fibration      257 340 353
Hopf fibration (generalized)      258
Horizontal      236
Horizontal, lift      244
Hyperbolic space      29 155 158 180
Hyperkahlerian      163 284 285 294 302 324 379 396 398
Hypersurface      320 362 423
Immersion      29 37
Incompressible      159
Index theorem      170 369 376
Infinitesimal automorphism      86
Infinitesimal complex deformation      361
Infinitesimal complex deformation (hermitian)      362 363
Infinitesimal complex deformation (symmetric)      363
Infinitesimal Einstein deformation      347 352 363
Infinitesimal observer      95
Instanton      371
Integrability condition      349 350
Integrable complex structure      68
Intersection form      161 367 368
Involution      295 296 299
Involutive distribution      282
Irreducible      357 363
Irreducible decomposition of curvature tensor      45
Irreducible isotropy      119
Irreducible symmetric space      119 297
Isometry      39
Isometry, group      39 41 178 180 181 192
Isotropy irreducible      119
Isotropy irreducible, space      7
Isotropy irreducible, spaces (tables of compact non symmetric strongly)      203
Isotropy irreducible, spaces(tables of non-compact non symmetric strongly)      204
Isotropy representation      178 182 187 197 204
Isotropy subgroup      178 191 195 296 298
Iwamoto — Lichnerowicz theorem      284
Iwasawa decomposition      180
Jacobi equations      107
Jacobi field      28 102 107 296
K3 surface      162 342 365 369 373 376 400
Kahler class      85
Kahler curvature      73
Kahler curvature, operator      73
Kahler form      70
Kahler metric      70
Kahler potential      85
Kahler — Einstein metric      319
Kahler — Einstein structures (space of)      365 367
Kahlerian      322
Kaluza — Klein      250 472
Killing vector field      35 40 183 334 346 377
Killing — Cartan form      184 185 198 298
Klein bottle      283
Kruskal model      111
Kulkarni — Nomizu product      47
Kummer surface      401
Lagrangian      116
Lagrangian (natural)      118
Laplacian      34
Laplacian (complex)      54
Laplacian (Dirac)      54
Laplacian (Hodge — de Rham)      35
Laplacian (Lichnerowicz)      54
Laplacian (rough)      52
Laplacian (twisted Dirac)      56
Lattice      368
Left-invariant Riemannian metric      182 190
Length      36
Levi form      85
Levi — Civita connection      30 182
Lichnerowicz Laplacian      54 132 133 347
Lie derivative      21
Light      109 110
Line      37 168 172
Linear connection      22 25
Linearization      62 346 462
Linearized Einstein equation      346
Link      159
Local solvability      469
Locally isometricly embeddable      145
Locally symmetric Lorentz manifold      206
Locally symmetric space      193 198 297 300 302 357
Loop      280
Lorentz Einstein metric      256
Lorentz geometry      96
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