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Gross M., Huybrechts D., Joyce D. — Calabi-Yau Manifolds and Related Geometries: Lectures at a Summer School in Nordfjordeid, Norway, June 2001 |
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Предметный указатель |
15 27—28
manifold 28
structure 27
genus 29
Almost Calabi — Yau m-folds 54
Associateive 3-folds 36 40 56
Associateive 3-folds deformations 41 56
Asymptotic cone 44 59
Atiyah — Singer index theorem 56
Beauville — Bogomolov form 173
Beauville — Bogomolov form of the generalized Kummer 179
Beauville — Bogomolov form of the Hilbert scheme 178
Beauville — Bogomolov form unnormalized 203
Berger's theorem 13—14
Bianchi identities 10 11
Calabi Conjecture 21—24
Calabi — Yau m-folds 15 18—19
Calabi — Yau m-folds almost 54
Calabi — Yau m-folds constructions 25 26
Calibrated geometry 32—36
Calibrated submanifolds 33
Calibrated submanifolds compact 50
Calibration 18 33
Calibration maximal 35
Canonical bundle 18
Cayley 4-folds 36 41 56
Cayley 4-folds deformations 41 56
Chern class 19
Coassociative 4-folds 36 40 55
Coassociative 4-folds deformations 41 56
Complete intersection 25
Complex manifold 16
Complex structure 16
Complex symplectic structure 20
Connection 7
Crepant resolution 26
Current, positive 197
Curvature 8
Curvature constant 13
Deformation 163
Deformation universal 164
Deformation unobstructed 165 194
Dolbeault cohomology 24
Exceptional holonomy groups 15 27—32
Exceptional holonomy groups compact manifolds 29—31
Fibration 161 185
FORM 7
Form holomorphic volume 18
Form Kaehler 17
Form Ricci 18
Geometric measure theory 32 33 36 58
Hilbert scheme 157 160
Hodge number 24
Holomorphyic volume form 18
Holonomy group and constant tensors 9
Holonomy group and curvature 9
Holonomy group of a connection 9
Holonomy group of a metric 11
Holonomy group properties 9
HRR-formula 178
Hyperkaehler geometry 15 20
Jacobi identity 11
K3 surface 24 155
K3 surface elliptic 156 162 186
K3 surface Fermat quartic 156
K3 surface Kummer surface 156
Kaehler class 17
Kaehler cone 169 197 211
Kaehler cone birational 214
Kaehler cone of a very general 191 198
Kaehler form 17
Kaehler geometry 15—17
Kaehler potential 17
Kodaira — Spencer class 163
Kodaira — Spencer class of the twistor space 189
Kummer variety, generalized 158 179 193 199
Lagrangian submanifolds 38
Legendrian index 60
| Levi-Civita connection 10
Lie bracket 7
Manifold hyperkaehler 169
Manifold, irreducible holomorphic symplectic 155
Manifold, irreducible holomorphic symplectic birational 158 161 166 192 203 208
Marked manifold 188
Metric 10
Metric Calabi — Yau 15
Metric Hermitian 17
Metric hyperkaehler 15 20
Metric irreducible 12
Metric Kaehler 15
Metric locally symmetric 13
Metric nonsymmetric 13
Metric product 12
Metric quaternionic Kaehler 15
Metric reducible 12
Minimal submanifolds 32—33
Mirror Symmetry 64—65
Moduli space 188
Moment map 42 45 49
Mukai 159 166 204
Nijenhuis tensor 16
Octonions 15
Parallel transport 9
Period domain 167 188 190
Period map 168 188
Period map surjectivity 190
Quaternions 15 20 38
Quintic 26
Resolution 26
Resolution crepant 26
Ricci curvature 18
Ricci form 18
Riemann curvature 10
Riemannian metric see metric
Special Lagrangian cones 42 58—61
Special Lagrangian cones rigid 61
Special Lagrangian cones, as an integrable system 44
Special Lagrangian cones, examples 47 48
Special Lagrangian fibrations 65—69
Special Lagrangian fibrations, discriminant 65 67
Special Lagrangian fibrations, singularities 66—69
Special Lagrangian m-folds 36—40
Special Lagrangian m-folds compact 51—55
Special Lagrangian m-folds in almost Calabi — Yau m-folds 54
Special Lagrangian m-folds ruled 44
Special Lagrangian m-folds strongly AC 58
Special Lagrangian m-folds weakly AC 58
Special Lagrangian m-folds with phase 37
Special Lagrangian m-folds, affine structures on moduli space 53—54
Special Lagrangian m-folds, Asymptotically Conical 58
Special Lagrangian m-folds, constructions 42—49
Special Lagrangian m-folds, deformations 39—40 50—52 59—60
Special Lagrangian m-folds, examples 47—49
Special Lagrangian m-folds, index of singularities 62 68
Special Lagrangian m-folds, obstructions 50 52—53
Special Lagrangian m-folds, singularities 50 57—63
Special Lagrangianbration 50
Spin(7) 15 28—29
Spin(7)-manifold 29
Spin(7)-structure 28
String theory 64
Symmetric space 12
SYZ Conjecture 63—69
Tangent cone 36 58
Tensors 6
Tensors, constant 9 11
Tensors, Einstein summation convention 7
Tensors, index notation 7
Torelli theorem global 192
Torelli theorem global for K3 surfaces 192
Torelli theorem global, counterexample 193
Torelli theorem local 168
Toric variety 26
Torsion 8
Twistor space 187
Vector bundles 6
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