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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.

Аннотация:

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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