Joyce D.D. — Compact Manifolds with Special Holonomy :: Электронная библиотека попечительского совета мехмата МГУ

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Joyce D.D. — Compact Manifolds with Special Holonomy

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Название: Compact Manifolds with Special Holonomy

Автор: Joyce D.D.

Аннотация:

Serving as both a graduate textbook on Reimannian holonomy groups and a research monograph on the exceptional holonomy groups Gc and Spin(7), this book is intended for mathematicians working in differential and Riemannian geometry and physicists working in String Theory. It's overall subject is Riemannian manifolds with special holonomy groups, especially Ricci-flat holonomy groups SU(m), Sp(m), G2, and Spin(7). Constructions and existence theorems are emphasized. Most proofs are given in full.

Язык:

Рубрика: Математика/Геометрия и топология/Алгебраическая и дифференциальная топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 436

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

space      5
$C^{k, \alpha}(M)$       see Hoelder space
holonomy      57—58 242—254
holonomy, associative 3-fold      70 264—265 326—327 417
holonomy, coassociative 4-fold      70 265—267 327—328 417
holonomy, compact manifolds, Betti numbers of      314 315 323 325 326 332—334 339
holonomy, compact manifolds, constructions      294—295 303—305
holonomy, compact manifolds, examples      309—326 329—338
holonomy, compact manifolds, finding $\pi_1(M)$       307—308
holonomy, compact manifolds, finding Betti numbers      308—309
holonomy, compact manifolds, moduli space of      251—254
holonomy, compact manifolds, topology of      245—247 306—309
holonomy, compact manifolds, with $\pi_1(M)\ne\{1\}$       314—315
holonomy, holonomy subgroups      245
holonomy, metrics Ricci-flat      244
holonomy, parallel spinors      245
holonomy, research problems      303—305 416—418
, definition      242
-manifold      243
-manifold, product      274
-manifold, QALE      272—278
-manifold, with holonomy SU(2)      271
-manifold, with holonomy SU(3)      272
-orbifolds $T^7/\Gamma$       278—280
-orbifolds $T^7/\Gamma$ , examples      312 315 316 329 334—337
-orbifolds $T^7/\Gamma$ , R-data      280—281
-orbifolds $T^7/\Gamma$ , resolutions of $T^7/\Gamma$       282—284
-structure      243
-structure, function $\Theta$       243 249
-structure, nearly parallel      269
-structure, positive 3-form      243
-structure, positive 4-form      243
-structure, small torsion      284 286
-structure, splitting of forms      244 245
-structure, torsion      243
-structure, torsion-free      243
      see Lebesgue space
      see Sobolev space
$\hat A$ -genus      67 164 259
$\mathbb H$       see quaternions
$\mathbb O$       see octonions
*      see Hodge star
Age grading      130—132 200
ALE manifold      173—174
ALE manifold, analysis on      178—182
ALE manifold, asymptotic coordinates      174
ALE manifold, Calabi conjecture for      186—188
ALE manifold, Eguchi — Hanson space      153—154 160
ALE manifold, examples      177—178 393—394
ALE manifold, Hodge theory      183—184
ALE manifold, holonomy Spin(7)      345—346
ALE manifold, hyperkaehler      148 153—155
ALE manifold, Kaehler      174 201
ALE manifold, radius function      174 175
ALE manifold, Ricci-flat Kaehler      175—178
ALE manifold, structure group Spin(7)      344 393—394
ALE manifold, weighted Hoelder space      176 179
ALE manifold, weighted Sobolev space      178
Ambrose — Singer Holonomy Theorem      32 37
Associative 3-fold      70 264—265 417
Associative 3-fold, examples      326—327
Asymptotically Locally Euclidean      see ALE manifold
Atiyah — Singer index theorem      19 67 259
Berger's theorem      55
Betti number      2
Betti number, refined      62 245 260
Bianchi identities      36 43 45 59
Blow-up      91—92 293
Bochner theorem      64 124
Bootstrap method      116 303 364
Calabi Conjecture      98—100
Calabi conjecture, for ALE manifolds      186—188
Calabi conjecture, for QALE manifolds      225 229
Calabi — Yau manifold      56 70 82 98 121—147 304
Calabi — Yau manifold, constructions      138—142 146
Calabi — Yau manifold, definition      123
Calabi — Yau manifold, deformations      142—144
Calabi — Yau manifold, Hodge numbers      125
Calabi — Yau orbifold      135 146 395—396 401—402
Calibrated geometry      68—70 264—269
Calibrated submanifold      68
Calibration      68
Canonical bundle      94
Cayley 4-fold      70 267—268 417
Cayley 4-fold, examples      371—373
Cayley numbers      see octonions
Characteristic class      94
Characteristic class, $\hat A$ -genus      67 164 259
Characteristic class, first Chern class      94 97 98 122
Characteristic class, first Pontryagin class      246—247 259 261
Cheeger — Gromoll Theorem      64
Chow's theorem      90 95 126
Coassociative 4-fold      70 265—267 417
Coassociative 4-fold, examples      327—328
Cohomology, deRham      2 182
Cohomology, Dolbeault      77
Cohomology, Hodge numbers      85
Cohomology, of sheaves      89 93
Cohomology, other cohomology theories      2
Cohomology, Poincare duality      3
Cohomology, with compact support      182
Compact linear map      6 103 179 187 226
Complete intersection      139 402 413
Complex manifold      72—75
Complex manifold, biholomorphism      74
Complex manifold, holomorphic function      72
Complex manifold, holomorphic map      74
Complex manifold, rigid      92 132 139
Complex projective space      73
Complex structure      72—73
Complex structure, almost      72
Complex symplectic manifold      162—164
Complex symplectic manifold, irreducible      162
Complex symplectic manifold, marked      163
Complex symplectic manifold, moduli space      163
Connection      20—25
Connection, Levi-Civita      40 42—43
Connection, on principal bundle      23
Connection, on tangent bundle      33—38
Connection, on vector bundle      22
Connection, torsion-free      35—38
Continuity method      104
Crepant resolution      126—132
Crepant resolution, of $\mathbb C^m / G$       175 210
Curvature and holonomy groups      32—33
Curvature in principal bundles      24
Curvature in vector bundles      22—23
Curvature of Kaehler metrics      81—82
Curvature, Ricci      44
Curvature, Riemann      43—44
Curvature, scalar      44
de Rham theorem      2
Deformation      92—93
Deformation, $\mathbb C^m / G$       132 201 238
Deformation, of Calabi — Yau manifold      142—144
Deformation, smoothing      92 313 318 324
Deformation, universal      93
Deformation, versal      93
Dirac operator      65—68 259 260
Divisor      96—97
Divisor, exceptional      91 127
Divisor, prime      96
Dolbeault cohomology      77
Douady space      166 215
Double point      127
Double point, ordinary      127
Double point, rational      129
Ebin's Slice Theorem      252
Eguchi — Hanson space      153—154 160 177 212 311 313 370 374
Elliptic equation, nonlinear      250

Elliptic operator      7—19
Elliptic operator, estimate      14
Elliptic operator, definition      9 11
Elliptic operator, existence of solutions      16—19
Elliptic operator, kernel finite-dimensional      17
Elliptic operator, nonlinear      10 100
Elliptic operator, regularity      13—16 297 303 364
Elliptic operator, Schauder estimate      14—15 180
Elliptic operator, symbol      9 11
Exterior form      see form
Fano manifold      168
FLOP      128
FORM      1—4
Form, complex symplectic      150
Form, G-structure splitting      59—60
Form, Hermitian      78
Form, holomorphic volume      122
Form, hyperkaehler 2-form      151
Form, Kaehler      79 122
Form, oftype (p, q)      77
Form, on Kaehler manifolds      82—84
Frobenius theorem      48
G-structure      38
Green's representation      14 181
Harmonic coordinates      298
Hilbert scheme      166 215
Hodge numbers      85
Hodge numbers, of hyperkaehler manifolds      164
Hodge star      3 60
Hodge star, on Kaehler manifolds      83
Hodge theory      4 61—63
Hodge theory, on ALE manifolds      183—184
Hodge theory, on Kaehler manifolds      84—85
Hoelder space      5—6
Hoelder space, weighted      176 179 221
Hoelder's inequality      4
Holomorphic vector bundle      77
Holonomy algebra      28 30 45
Holonomy group and cohomology      59—64
Holonomy group and curvature      32—33
Holonomy group, classification      55—59
Holonomy group, constant tensors      34—35
Holonomy group, definition      26 29 45
Holonomy group, exceptional      see $G_2$

holonomy; Spin(7) holonomy etc.
Holonomy group, for principal bundles      29—32
Holonomy group, for vector bundles      23—29
Holonomy group, restricted      28 29 43
Holonomy group, Ricci-flat      58
Holonomy group, Riemannian      44—45
Hypercomplex algebraic geometry      171 213
Hypercomplex manifold      148 167 170
Hyperkaehler manifold      57 98 148—167 169
Hyperkaehler manifold, ALE      148 153—155
Hyperkaehler manifold, examples      165—167
Hyperkaehler manifold, Hodge numbers      164
Hyperkaehler manifold, moduli space      165
Hyperkaehler manifold, QALE      211 213—215 239
Hyperkaehler manifold, twistor space      151—152
Hyperkaehler quotient      154 169
Hyperkaehler structure      148 151
Hypersurface      96
Hypersurface, Calabi — Yau      139
Hypersurface, degree d      139
Hypersurface, in toric variety      142
Hypersurface, in weighted projective space      140 401
Implicit Mapping Theorem      7 253 263
Injectivity radius      5 221 292—295 298 359—361 399
Instanton      169 269
Interior estimate      16
Intrinsic torsion      40
Inverse mapping theorem      7 118 228
K3 surface      155—162
K3 surface, examples      156
K3 surface, marked      157
K3 surface, moduli space      157 161
Kaehler chamber      158
Kaehler class      80 85 175 210
Kaehler cone      85 158 175 210
Kaehler form      79 122
Kaehler manifold      56
Kaehler metric      79
Kaehler potential      80
Kaehler potential type      215 229
Kodaira embedding theorem      96 125
Kondrakov Theorem      7 16 103
Kummer construction      137 156—157 160—161
Kuranishi family      94 143
Laplacian      3 7 10 14 61
Laplacian, on ALE manifolds      180—182 *
Laplacian, on Kaehler manifolds      83 105 198
Laplacian, on QALE manifolds      220—225
Lebesgue space      4—5
Lefschetz hyperplane theorem      97 140 404
Levi-Civita connection      40 42—43
Line bundle      94—96
Line bundle, ample      95 125
Line bundle, canonical      94 122 126
Line bundle, first Chern class      94 97 98 122
Line bundle, over $\mathbb{CP}^m$       94
Line bundle, positive      96
Line bundle, very ample      95
Maximum principle      16 222
McKay correspondence      129 131 154 309
Metric, Fubini-Study      53 80
Metric, Hermitian      78
Metric, hyperkaehler      151
Metric, Kaehler      79
Metric, reducible      46—50
Metric, symmetric      50—55
Mirror Symmetry      142 145—146
Moduli space      63 169
Moduli space of -manifolds      251—254
Moduli space of complex symplectic manifolds      163
Moduli space of hyperkaehler manifolds      165
Moduli space of K3 surfaces      157 161
Moduli space of Spin(7)-manifolds      261—264
Monge — Ampere equation      100
Newlander — Nirenberg theorem      72
Nijenhuis tensor      72
Node      127
Octonions      57
Orbifold      132—136
Orbifold, Calabi — Yau      135 146 395—396 401^102
Orbifold, complex      133 166
Orbifold, crepant resolution      136—139
Orbifold, group      133
Orbifold, Kaehler      134
Orbifold, of torus      137 278—280 346—347
Orbifold, point      133
Orbifold, real      133
Parallel transport      26
Period domain      158 163
Period domain, hyperkaehler      161 165
Period map      143 157 163
Period map, hyperkaehler      161 165
Picard group      94
Poincarg duality      3
Principal bundle      20
Principal bundle, connection      23
QALE manifold, analysis on      219—225
QALE manifold, Calabi conjecture for      225 229
QALE manifold, definition      208 236—238
QALE manifold, examples      212—215 239—241 276—278
QALE manifold, generalized      235—241
QALE manifold, holonomy       277—278
QALE manifold, holonomy Sp(m)      211 213—215 239
QALE manifold, holonomy Spin(7)      345—346
QALE manifold, holonomy SU(m)      211—213 239
QALE manifold, Kaehler      208—210 238
QALE manifold, Kaehler potentials      215

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