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| Kobayashi S., Nomizu K. — Foundations of Differential Geometry, Volume 2 |
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| Предметный указатель |
(+)-connection 198
(0)-connection 199
(—)-connection 199
1-parameter group of transformations I-12
1-parameter subgroup I-39
Abelian Lie algebra 325
Abelian variety 131
Absolute parallelism I-122
Adapted frame 2 54
Adjoint representation I-40
Affine connection I-129
Affine connection, generalised I-127
Affine connection, invariant 375
Affine connection, invariant by parallelism 194
Affine connection, rigid 376
Affine frame I-126
Affine holonomy group I-130 331
Affine locally symmetric 222
Affine mapping I-225
Affine parallel displacement I-130
Affine parameter I-138
Affine space I-125
Affine space, tangent I-125
Affine symmetric 223
Affine transformation I-125 I-226
Affine transformation, infinitesimal I-230
Allowable imbedding 52
Almost cocomplex structure 383
Almost complex connection 143
Almost complex manifold 121
Almost complex manifold, natural orientation of 121
Almost complex mapping 122 127
Almost complex structure 121
Almost complex structure on spheres 138—140
Almost complex structure, conjugate 123
Almost complex structure, integrability of 124 321
Almost complex structure, integrable 124 321
Almost complex structure, invariant 216
Almost complex structure, torsion of 123
Almost effective action 187
Almost Hamiltonian manifold 149
Almost hermitian manifold 147
Almost Kaehler manifold 149
Almost product structure 384
Almost symplectic manifold 149
Alternation I-28
Analytic continuation I-254
Arc-length I-157
Atlas I-2
Atlas, complete I-2
Augmented index 89
Auto-parallel submanifold 53
Automorphism of a connection I-81
Automorphism of a G—structure I-307 186 333
Automorphism of a Lie algebra I-40
Automorphism of a Lie group I-40
Automorphism of an almost complex structure 127
Bergman metric 163
Bianchi's identities I-78 I-121 I-135
Bonnet's theorem 78
Bounded domain 162 375
Bounded domain, symmetric 263
Bundle holonomy I-85
Bundle homomorphism of I-53
Bundle of adapted frames 2 54
Bundle of affine frames I-126
Bundle of complex linear frames 141
Bundle of normal frames 2
Bundle of orthonormal frames I-60
Bundle of unitary frames 152
Bundle vector I-113
Bundle vector, Hermitian 178
Bundle vector, orientable, oriented 314
Bundle vector, Riemannian 315
Bundle, associated I-55
Bundle, induced I-60
Bundle, normal 3
Bundle, principal fibre I-50
Bundle, reduced I-53
Bundle, sub- I-53
Bundle, tangent I-56
Bundle, tensor I-56
Bundle, trivial I-50
C-space 138 373
Canonical 1-form on a group I-41
Canonical complex structure 115
Canonical connection I-110 I-301 7 230
Canonical connectionon a symmetric space 230
Canonical decomposition (= de Rham decomposition) I-185 I-192 171 246 263 331
Canonical decomposition of a symmetric Lie algebra 226
Canonical flat connection I-92
Canonical form on L(M) I-118
Canonical Hermitian form 374
Canonical invariant connection I-110 I-301 192 230
Canonical invariant Riemannian metric I-155
Canonical linear connection I-302
Canonical metric I-155
Canonical parameter of a geodesic I-162
Cayley numbers 139
Center of gravity 109
Characteristic class 293
Chart I-2
Chern character 311
Chern class 305
Christoffel's symbols ( ) I-141
Clifford translation 105
Codazzi, equation of 25—26
Compact real form 291
Compact type, Lie algebra of 204 252 329
Compact type, symmetric Lie algebra of 252
Compact type, symmetric space of 252 256
Compact-open topology I-46
Comparison theorem of Rauch 76
Complete linear connection I-134
Complete Riemannian manifold I-172
Complete Riemannian metric I-172
Complete vector field I-13
Complex affine (locally) symmetric 259
Complex conjugation 116
Complex contact form 385
Complex differential form 124 125
Complex differential form, holomorphic 129
Complex Grassmann manifold 133 160 286
Complex homogeneous space 220 373
Complex hyperbolic space 282
Complex hypersurface 378 379
Complex Lie algebra 120 329
Complex Lie group 130
Complex linear frame 141
Complex manifold I-3 121
Complex parallelizable 132 373
Complex projective space 134 159 273
Complex quadric 278 378
Complex structure (on a manifold) 122
Complex structure (on a vector space) 114
Complex submanifold 164 175 378
Complex tangent space 124
Complex tangent vector 124
Complex tangent vectorof type (1, 0) or (0, 1) 125
Complex torus 131 159
Complexification of a Lie algebra 329
Complexification of a vector space 116
Components of a 1-form I-6
Components of a linear connection I-141
Components of a tensor (field) I-21 I-26
Components of a vector (field) I-5
Conformal transformation I-309
Conformal transformation infinitesimal I-309
Conjugate almost complex structure 123
Conjugate complex manifold 123
| Conjugate point 67 71
Conjugate point, multiplicity of 88
Connection I-63
Connection in normal bundle 4 15
Connection, (+)- 198
Connection, (0)- 199
Connection, (—)- 198
Connection, affine I-129
Connection, canonical I-110 I-301 7 230
Connection, canonical flat I-92
Connection, canonical invariant I-110 I-301 192 230
Connection, canonical linear connection I-302
Connection, flat I-92
Connection, form I-64
Connection, generalized affine I-127
Connection, Hermitian 178
Connection, induced I-82
Connection, invariant I-81 I-103 376
Connection, invariant by parallelism I-262 194
Connection, Levi-Civita I-158
Connection, linear I-119
Connection, metric I-117 I-158
Connection, natural torsion-free 197
Connection, normal invariant 208
Connection, Riemannian I-158
Connection, torsion-free 332^
Connection, universal I-290 332
Constant curvature I-202
Constant curvature, space of I-202 I-204 24 71 264 268
Constant curvature, surface of 343
Constant holomorphic sectional curvature 168
Constant holomorphic sectional curvature, space of 134 159 169 282
Contact form 381
Contact form complex 385
Contact structure 381
Contact structure, almost 382
Contact structure, complex 385
Contraction I-22
Contravariant tensor (space) I-20
Convex hypersurface 40
Convex hypersurface strictly 40
Convex neighborhood I-149 I-166
Coordinate neighborhood I-3
Covariant derivative I-114 I-115 I-122
Covariant differential I-124
Covariant differentiation I-115 I-116 I-123
Covariant tensor (space) I-20
Covector I-6
Covering space I-61
Critical point 362
Critical point, index of 362
Critical point, non-degenerate 362
Cross section I-57
Cross section, adapted to a normal coordinate system I-257
Cubic neighborhood I-3
Curvature I-132
Curvature form I-77
Curvature Gaussian (Gauss — Kronecker) 33
Curvature operator 367
Curvature tensor (field) I-132 I-145
Curvature tensor (field), Riemannian I-201
Curvature, constant I-202
Curvature, holomorphic bisectional 372
Curvature, holomorphic sectional 168
Curvature, Kaehlerian sectional 369
Curvature, mean 33
Curvature, principal 32
Curvature, recurrent I-305
Curvature, scalar I-294
Curvature, sectional I-202
Curvature, total 362
Curvature, transformation I-133
Cut locus 100
Cut point 96
Cylinder I-223
Cylinder Euclidean I-210
Cylinder twisted I-223
de Rham decomposition I-185 I-192 171 246 263 331
Degree (p, q) 125
Derivation of  (M) I-33
Derivation of  (M) I-30
Derivation of tensor algebra I-25
Derived series of a Lie algebra 325
Descending central series of a Lie algebra 325
Development I-131
Diffeomorphism I-9
Differential form I-6 I-7
Differential form, complex 124 125
Differential form, holomorhpic 129
Differential of a function I-8
Differential of a mapping I-8
Differential, covariant I-124
Direct product of symmetric spaces 228
Direct sum of symmetric Lie algebras 228
Discontinuous group I-44
Discontinuous group properly I-43
Distance function I-157
distribution I-10
Distribution, involutive I-10
Divergence I-281 337
Dual symmetric Lie algebra 253
Effective action of a group I-42 187
Effective action of a group almost 187
Effective symmetric Lie algebra 226
Effective symmetric space 225
Effective symmetric space, almost 225
Einstein hypersurface 36 378
Einstein manifold I-294 336 341
Elliptic linear Lie algebra 334
Elliptic space form I-209 264
Equation of Codazzi 25 26 47
Equation of Gauss 23 26
Equation of Jacobi 63
Equivalence problem I-256 357
Equivariant isometric imbedding 356
Euclidean cylinder I-210
Euclidean locally I-197 I-209 I-210
Euclidean metric I-154
Euclidean motion I-215
Euclidean subspace I-218
Euclidean tangent space I-193
Euclidean torus I-210
Euler class 314
Exponential mapping I-39 I-140 I-147
Exterior, covariant derivative I-77
Exterior, covariant differentiation I-77
Exterior, derivative I-7 I-36
Exterior, differentiation I-7 I-36
Fibre I-55
Fibre, bundle, principal I-50
Fibre, metric I-116
Fibre, transitive I-106
Finite type, linear Lie algebra of 333
First normal space 353
Flat affine connection I-209
Flat connection I-92
Flat connection, canonical I-92
Flat linear connection I-210
Flat Riemannian manifold I-209 I-210
Form 1-form I-6
Form curvature I-77
Form r-form I-7
Form torsion I-120
Form, tensorial I-75
Form, tensorial pseudo- I-75
Frame, adapted 2 54
Frame, affine I-126
Frame, complex linear 141
Frame, linear I-55
Frame, normal 2
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