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| Kobayashi S., Nomizu K. — Foundations of Differential Geometry, Volume 2 |
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| Предметный указатель |
Frame, orthonormal I-60
Frame, unitary 152
Free action of a group I-42
Frobenius, theorem of I-10 323
Fubini — Study metric 160 274
Fundamental 2-form of a Hermitian manifold 147
Fundamental theorem for hypersurfaces 47
Fundamental vector field I-51
G-structure I-288 332 333
Gauss formula 15 18
Gauss theorema egregium of 33
Gauss — Bonnet theorem 318 358
Gauss, equation of 23 26 47
Gauss, spherical map of 9 18
Gaussian (Gauss — Kronecker) curvature 33
Geodesic I-131 I-146
Geodesic, minimizing I-166
Geodesic, totally I-180 54
Gradient 337
Grassmann manifold 6 9 271
Grassmann manifold of oriented p-planes 9 272
Grassmann manifold, complex 133 160 286
Grassmann manifold, oriented 272
Green's theorem I-281
Hamiltonian manifold 149
Hamiltonian manifold, almost 149
Harmonic function 339
Hermitian connection 178
Hermitian inner product 118
Hermitian locally symmetric 259
Hermitian manifold 147
Hermitian metric 146
Hermitian symmetric 259
Hermitian vector bundle 178
Holomorphic I-2
Holomorphic bisectional curvature 372
Holomorphic form 129
Holomorphic sectional curvature 168
Holomorphic transformation 336
Holomorphic vector field 129
Holonomy bundle I-85
Holonomy group I-71 I-72
Holonomy group of a Kaehler manifold 173
Holonomy group of a submanifold 355
Holonomy group, affine I-130
Holonomy group, homogeneous I-130
Holonomy group, infinitesimal I-96 I-151
Holonomy group, linear I-130
Holonomy group, local I-94 I-151
Holonomy group, restricted I-71 I-72
Holonomy theorem I-85
Homogeneous complex manifold 220 373
Homogeneous coordinate system 134
Homogeneous holonomy group I-130
Homogeneous Kaehler manifold 374 376
Homogeneous Riemannian manifold I-155 I-176 200 208 211 376
Homogeneous space I-43
Homogeneous space, complex 220
Homogeneous space, Kaehlerian 374 376
Homogeneous space, naturally reductive 202
Homogeneous space, reductive 190 376
Homogeneous space, symmetric I-301 225
Homogeneous strongly curvature 357
Homomorphistn of fibre bundle I-53
Homomorphistn of symmetric Lie algebra 227
Homomorphistn of symmetric space 227
Homothetic 289
Homothetic transformation I-242 I-309
Hopf manifold 137
Hyperbolic space form I-209 268
Hyperbolic space form, complex 282
Hypersurface 5
Hypersurface in a Euclidean space 17 29
Hypersurface, Codazzi equation of 26 30
Hypersurface, complex 378
Hypersurface, Einstein 36
Hypersurface, fundamental theorem for 47
Hypersurface, Gauss equation of 23 24 30
Hypersurface, Gaussian curvature of 33
Hypersurface, mean curvature of 33
Hypersurface, principal curvature of 32
Hypersurface, Ricci tensor of 35
Hypersurface, rigidity of 45
Hypersurface, second fundamental form of 13
Hypersurface, spherical map of 9
Hypersurface, type number of 42
Imbedding I-9 I-53
Imbedding, isometric I-161 354
Imbedding, isometric equivariant 356
Immersion I-9
Immersion, isometric I-161 354
Immersion, Kaehlerian 164
Immersion, minimal (in mean curvature) 376
Immersion, minimal (in total curvature) 363
Indefinite Riemannian metric I-155
Indefinite Riemannian metric, invariant 200
INDEX 89
Index form 81
Index of a critical point 362
Index of nullity 347
Index of relative nullity 348
Index theorem (of Morse) 89
Index, augmented 89
Induced bundle I-60
Induced connection I-82
Induced Riemannian metric I-154
Infinite type, linear Lie algebra of 333
Infinitesimal affine transformation I-230
Infinitesimal automorphism of a G-structure 186
Infinitesimal automorphism of an almost complex structure 127
Infinitesimal holonomy group I-96 I-151
Infinitesimal isometry I-237
Infinitesimal variation of a geodesic 63
Inhomogeneous coordinate system 134
Inner product I-24
Integrability conditions of almost complex structure 125 145 321 324
Integrable almost complex structure 124 321 324
Integral curve I-12
Integral manifold I-10
Interior product I-35
Invariant affine connection 375
Invariant almost complex structure 216
Invariant by parallelism I-262 194
Invariant connection I-81 I-103 375
Invariant indefinite Riemannian metric 200
Invariant polynomial 293 298
Invariant Riemannian metric I-154
Involutive distribution I-10
Involutive Lie algebra 225
Involutive Lie algebra, orthogonal 246
Irreducible group of Euclidean motions I-218
Irreducible Riemannian manifold I-179
Irreducible symmetric Lie algebra 252
Irreducible weakly 331
Isometric I-161
Isometric imbedding I-161 354 355 356 379
Isometric imbedding, equivariant 356
Isometric immersion I-161 354 355
Isometry I-46 I-161 I-236 335
Isometry infinitesimal I-237
Isotropy group, linear I-154 187
Isotropy subgroup I-49
Jacobi equation 63
Jacobi field 63 68
Kaehler manifold 149
Kaehler manifold, almost 149
Kaehler manifold, pseudo 149
Kaehler metric 149
Kaehler non-degenerate 175
Kaehlerian homogeneous 374 376
| Kaehlerian pinching 369
Kaehlerian sectional curvature 369
Killing vector field I-237
Killing — Cartan form I-155 252 325
Killing — Cartan form of a symmetric Lie algebra 250
Killing — Cartan form of o(n + 1) 266
Killing — Cartan form of o(n, 1) 270
Klein bottle I-223
Laplacian 338
Lasso I-73 I-184 I-284
Leibniz's formula I-11
length function 79
Levi decomposition 238 327
Levi subalgebra 327
Levi-Civita connection I-158
Lie algebra of (non) compact type 204 252 329
Lie algebra, abelian 325
Lie algebra, complex 120 329
Lie algebra, dual symmetric 253
Lie algebra, effective symmetric 226
Lie algebra, involutive 225
Lie algebra, irreducible symmetric 252
Lie algebra, nilpotent 325
Lie algebra, orthogonal symmetric 246
Lie algebra, reductive 326
Lie algebra, semi-simple 325
Lie algebra, simple 325
Lie algebra, solvable 325
Lie algebra, symmetric 225 238
Lie derivative I-29
Lie differentiation I-29
Lie group I-38
Lie group, complex 130
Lie subgroup I-39
Lie transformation group I-41
Lie triple system 237
Lift I-64 I-68 I-88
Lift horizontal I-64 I-68 I-88
Lift natural I-230
Linear connection I-119
Linear frame I-55
Linear frame complex 141
Linear holonomy group I-130
Linear isotropy group I-154 187
Linear isotropy representation 187
Local basis of a distribution I-10
Local coordinate system I-3
Locally affine I-210
Locally Euclidean I-197 I-209 I-210
Locally symmetric I-303 222 243 259
Lorentz group 268
Lorentz manifold (metric) I-292 I-297
Manifold I-2 I-3
Manifold, complex (analytic) I-3 121
Manifold, differentiable I-2 I-3
Manifold, Hermitian 147
Manifold, Kaehler 149
Manifold, oriented, orientable I-3
Manifold, real analytic I-2
Manifold, sub- I-9
Manifold, symplectic 149
Maurer — Cartan equations of I-41
Maximal nilpotent ideal 325
Mean curvature 33
Mean curvature, constant 346
Mean curvature, normal 34 340 341
Metric connection I-117 I-158
Minimal immersion (in mean curvature) 379
Minimal immersion (in total curvature) 363
Minimal submanifold 34 340 342 379
Minimum point 96
Moebius band I-223
Multiplicity of a conjugate point 88
Multiplicity of an index form 89
n-frame 6
Natural lift of a vector field I-230
Natural torsionfree connection 197
Naturally reductive homogeneous space 202
Nilpotent Lie algebra 325
Non-compact type, Lie algebra of 204 252
Non-compact type, symmetric Lie algebra of 252
Non-compact type, symmetric space of 252 256
Non-degenerate Kaehler manifold 173
Non-positive curvature, space of 29 70 102 109
Non-prolongeable I-178
Normal bundle 3
Normal coordinate system I-148 I-162
Normal frame 2
Normal invariant connection 208
Normal space 2
Nullity of a bilinear form 89
Nullity, index of 347
Nullity, index of relative 348
Orbit I-12
Orientable, oriented, vector bundle 314
Orientation I-3
Orientation, natural 121
Orthogonal symmetric Lie algebra 246
Orthogonal symmetric Lie algebra of (non) compact type 252
Orthonormal frame I-60
Ovaloid 346
Paracompact I-58
Parallel affine I-130
Parallel cross section I-88
Parallel displacement I-70 I-37 I-88
Parallel tensor field I-124
Parallelism, absolute I-122
Parallelism, complex 132 373
Parallelism, invariant by I-262 194
Partition of unity I-272
Pinched, pinching 364 369
Pinched, pinching, Holomorphic 369
Pinched, pinching, Kaehlerian 369
Point field I-131
Polynomial function 298
Polynomial function invariant 293 298
Pontrjagin class 312
Positive curvature, space of 74 78 88 364
Positive Ricci tensor, space of 74 88
Principal curvature 32
Principal direction 32
Projectable vector field 218
Projection, covering I-50
Projective space I-52 134 159
Prolongation (of linear Lie algebra) 333
Properly discontinuous I-43
Pseudo-conformal transformation 335
Pseudo-group of transformations I-1 I-2
Pseudo-Kaehler manifold 149
Pseudo-tensorial form I-75
Quotient space I-43 I-44
Radical of a Lie algebra 238 325
Radon measure 108
Rank of a mapping I-8
Rauch, comparison theorem of 76
Real form of a complex Lie algebra 291 330
Real projective space I-52
Real representation of GL(n; C) 115
Real representation of SL(n; C) 151
Recurrent curvature I-305
Recurrent tensor I-304
Reduced bundle I-53
Reducible connection I-81 I-83
Reducible Riemannian manifold I-179
Reducible structure group I-53
Reduction of connection I-81 I-83
Reduction of structure group I-53
Reduction Theorem I-83
Reductive homogeneous space 190
Reductive homogeneous space naturally 202
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