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Joyce D.D. Ч Compact Manifolds with Special Holonomy
Joyce D.D. Ч Compact Manifolds with Special Holonomy

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Ќазвание: Compact Manifolds with Special Holonomy

јвтор: Joyce D.D.

јннотаци€:

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: en

–убрика: ћатематика/√еометри€ и топологи€/јлгебраическа€ и дифференциальна€ топологи€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2000

 оличество страниц: 436

ƒобавлена в каталог: 16.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$C^k$ space      5
$C^{k, \alpha}(M)$      see Hoelder space
$G_2$ holonomy      57Ч58 242Ч254
$G_2$ holonomy, associative 3-fold      70 264Ч265 326Ч327 417
$G_2$ holonomy, coassociative 4-fold      70 265Ч267 327Ч328 417
$G_2$ holonomy, compact manifolds, Betti numbers of      314 315 323 325 326 332Ч334 339
$G_2$ holonomy, compact manifolds, constructions      294Ч295 303Ч305
$G_2$ holonomy, compact manifolds, examples      309Ч326 329Ч338
$G_2$ holonomy, compact manifolds, finding $\pi_1(M)$      307Ч308
$G_2$ holonomy, compact manifolds, finding Betti numbers      308Ч309
$G_2$ holonomy, compact manifolds, moduli space of      251Ч254
$G_2$ holonomy, compact manifolds, topology of      245Ч247 306Ч309
$G_2$ holonomy, compact manifolds, with $\pi_1(M)\ne\{1\}$      314Ч315
$G_2$ holonomy, holonomy subgroups      245
$G_2$ holonomy, metrics Ricci-flat      244
$G_2$ holonomy, parallel spinors      245
$G_2$ holonomy, research problems      303Ч305 416Ч418
$G_2$, definition      242
$G_2$-manifold      243
$G_2$-manifold, product      274
$G_2$-manifold, QALE      272Ч278
$G_2$-manifold, with holonomy SU(2)      271
$G_2$-manifold, with holonomy SU(3)      272
$G_2$-orbifolds $T^7/\Gamma$      278Ч280
$G_2$-orbifolds $T^7/\Gamma$, examples      312 315 316 329 334Ч337
$G_2$-orbifolds $T^7/\Gamma$, R-data      280Ч281
$G_2$-orbifolds $T^7/\Gamma$, resolutions of $T^7/\Gamma$      282Ч284
$G_2$-structure      243
$G_2$-structure, function $\Theta$      243 249
$G_2$-structure, nearly parallel      269
$G_2$-structure, positive 3-form      243
$G_2$-structure, positive 4-form      243
$G_2$-structure, small torsion      284 286
$G_2$-structure, splitting of forms      244 245
$G_2$-structure, torsion      243
$G_2$-structure, torsion-free      243
$L^p(M)$      see Lebesgue space
$L^p_k(M)$      see Sobolev space
$\hat A$-genus      67 164 259
$\mathbb H$      see quaternions
$\mathbb O$      see octonions
*      see Hodge star
Age grading      130Ч132 200
ALE manifold      173Ч174
ALE manifold, analysis on      178Ч182
ALE manifold, asymptotic coordinates      174
ALE manifold, Calabi conjecture for      186Ч188
ALE manifold, Eguchi Ч Hanson space      153Ч154 160
ALE manifold, examples      177Ч178 393Ч394
ALE manifold, Hodge theory      183Ч184
ALE manifold, holonomy Spin(7)      345Ч346
ALE manifold, hyperkaehler      148 153Ч155
ALE manifold, Kaehler      174 201
ALE manifold, radius function      174 175
ALE manifold, Ricci-flat Kaehler      175Ч178
ALE manifold, structure group Spin(7)      344 393Ч394
ALE manifold, weighted Hoelder space      176 179
ALE manifold, weighted Sobolev space      178
Ambrose Ч Singer Holonomy Theorem      32 37
Associative 3-fold      70 264Ч265 417
Associative 3-fold, examples      326Ч327
Asymptotically Locally Euclidean      see ALE manifold
Atiyah Ч 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      91Ч92 293
Bochner theorem      64 124
Bootstrap method      116 303 364
Calabi Conjecture      98Ч100
Calabi conjecture, for ALE manifolds      186Ч188
Calabi conjecture, for QALE manifolds      225 229
Calabi Ч Yau manifold      56 70 82 98 121Ч147 304
Calabi Ч Yau manifold, constructions      138Ч142 146
Calabi Ч Yau manifold, definition      123
Calabi Ч Yau manifold, deformations      142Ч144
Calabi Ч Yau manifold, Hodge numbers      125
Calabi Ч Yau orbifold      135 146 395Ч396 401Ч402
Calibrated geometry      68Ч70 264Ч269
Calibrated submanifold      68
Calibration      68
Canonical bundle      94
Cayley 4-fold      70 267Ч268 417
Cayley 4-fold, examples      371Ч373
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      246Ч247 259 261
Cheeger Ч Gromoll Theorem      64
Chow's theorem      90 95 126
Coassociative 4-fold      70 265Ч267 417
Coassociative 4-fold, examples      327Ч328
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      72Ч75
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      72Ч73
Complex structure, almost      72
Complex symplectic manifold      162Ч164
Complex symplectic manifold, irreducible      162
Complex symplectic manifold, marked      163
Complex symplectic manifold, moduli space      163
Connection      20Ч25
Connection, Levi-Civita      40 42Ч43
Connection, on principal bundle      23
Connection, on tangent bundle      33Ч38
Connection, on vector bundle      22
Connection, torsion-free      35Ч38
Continuity method      104
Crepant resolution      126Ч132
Crepant resolution, of $\mathbb C^m / G$      175 210
Curvature and holonomy groups      32Ч33
Curvature in principal bundles      24
Curvature in vector bundles      22Ч23
Curvature of Kaehler metrics      81Ч82
Curvature, Ricci      44
Curvature, Riemann      43Ч44
Curvature, scalar      44
de Rham theorem      2
Deformation      92Ч93
Deformation, $\mathbb C^m / G$      132 201 238
Deformation, of Calabi Ч Yau manifold      142Ч144
Deformation, smoothing      92 313 318 324
Deformation, universal      93
Deformation, versal      93
Dirac operator      65Ч68 259 260
Divisor      96Ч97
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 Ч Hanson space      153Ч154 160 177 212 311 313 370 374
Elliptic equation, nonlinear      250
Elliptic operator      7Ч19
Elliptic operator, $L^p$ estimate      14
Elliptic operator, definition      9 11
Elliptic operator, existence of solutions      16Ч19
Elliptic operator, kernel finite-dimensional      17
Elliptic operator, nonlinear      10 100
Elliptic operator, regularity      13Ч16 297 303 364
Elliptic operator, Schauder estimate      14Ч15 180
Elliptic operator, symbol      9 11
Exterior form      see form
Fano manifold      168
FLOP      128
FORM      1Ч4
Form, complex symplectic      150
Form, G-structure splitting      59Ч60
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      82Ч84
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 61Ч63
Hodge theory, on ALE manifolds      183Ч184
Hodge theory, on Kaehler manifolds      84Ч85
Hoelder space      5Ч6
Hoelder space, weighted      176 179 221
Hoelder's inequality      4
Holomorphic vector bundle      77
Holonomy algebra      28 30 45
Holonomy group and cohomology      59Ч64
Holonomy group and curvature      32Ч33
Holonomy group, classification      55Ч59
Holonomy group, constant tensors      34Ч35
Holonomy group, definition      26 29 45
Holonomy group, exceptional      see $G_2$ holonomy; Spin(7) holonomy etc.
Holonomy group, for principal bundles      29Ч32
Holonomy group, for vector bundles      23Ч29
Holonomy group, restricted      28 29 43
Holonomy group, Ricci-flat      58
Holonomy group, Riemannian      44Ч45
Hypercomplex algebraic geometry      171 213
Hypercomplex manifold      148 167 170
Hyperkaehler manifold      57 98 148Ч167 169
Hyperkaehler manifold, ALE      148 153Ч155
Hyperkaehler manifold, examples      165Ч167
Hyperkaehler manifold, Hodge numbers      164
Hyperkaehler manifold, moduli space      165
Hyperkaehler manifold, QALE      211 213Ч215 239
Hyperkaehler manifold, twistor space      151Ч152
Hyperkaehler quotient      154 169
Hyperkaehler structure      148 151
Hypersurface      96
Hypersurface, Calabi Ч 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 292Ч295 298 359Ч361 399
Instanton      169 269
Interior estimate      16
Intrinsic torsion      40
Inverse mapping theorem      7 118 228
K3 surface      155Ч162
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 156Ч157 160Ч161
Kuranishi family      94 143
Laplacian      3 7 10 14 61
Laplacian, on ALE manifolds      180Ч182 *
Laplacian, on Kaehler manifolds      83 105 198
Laplacian, on QALE manifolds      220Ч225
Lebesgue space      4Ч5
Lefschetz hyperplane theorem      97 140 404
Levi-Civita connection      40 42Ч43
Line bundle      94Ч96
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      46Ч50
Metric, symmetric      50Ч55
Mirror Symmetry      142 145Ч146
Moduli space      63 169
Moduli space of $G_2$-manifolds      251Ч254
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      261Ч264
Monge Ч Ampere equation      100
Newlander Ч Nirenberg theorem      72
Nijenhuis tensor      72
Node      127
Octonions      57
Orbifold      132Ч136
Orbifold, Calabi Ч Yau      135 146 395Ч396 401^102
Orbifold, complex      133 166
Orbifold, crepant resolution      136Ч139
Orbifold, group      133
Orbifold, Kaehler      134
Orbifold, of torus      137 278Ч280 346Ч347
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      219Ч225
QALE manifold, Calabi conjecture for      225 229
QALE manifold, definition      208 236Ч238
QALE manifold, examples      212Ч215 239Ч241 276Ч278
QALE manifold, generalized      235Ч241
QALE manifold, holonomy $G_2$      277Ч278
QALE manifold, holonomy Sp(m)      211 213Ч215 239
QALE manifold, holonomy Spin(7)      345Ч346
QALE manifold, holonomy SU(m)      211Ч213 239
QALE manifold, Kaehler      208Ч210 238
QALE manifold, Kaehler potentials      215
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