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Kobayashi S., Nomizu K. — Foundations of Differential Geometry, Volume 2
Kobayashi S., Nomizu K. — Foundations of Differential Geometry, Volume 2

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Название: Foundations of Differential Geometry, Volume 2

Авторы: Kobayashi S., Nomizu K.


This two-volume introduction to differential geometry, part of Wiley's popular Classics Library, lays the foundation for understanding an area of study that has become vital to contemporary mathematics. It is completely self-contained and will serve as a reference as well as a teaching guide. Volume 1 presents a systematic introduction to the field from a brief survey of differentiable manifolds, Lie groups and fibre bundles to the extension of local transformations and Riemannian connections. The second volume continues with the study of variational problems on geodesics through differential geometric aspects of characteristic classes. Both volumes familiarize readers with basic computational techniques.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 470

Добавлена в каталог: 17.04.2008

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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 ($\Gamma^i_{jk}$)      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 $\mathfrak{D}$(M)      I-33
Derivation of $\mathfrak{T}$(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
1 2 3
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