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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
Reductive Lie algebra      326
Reductive subalgebra      326
Restriction of tensor field      57 58
Ricci form      153 183
Ricci tensor      I-248 I-292 35
Ricci tensor of a Kaehler manifold      149
Riemannain canonical invariant      I-155
Riemannain canonical invariant, indefinite      I-155
Riemannain canonical invariant, induced      I-154
Riemannain canonical invariant, invariant      I-154
Riemannain connection      I-158
Riemannain curvature tensor      I-201
Riemannain homogeneous space      I-155 I-176 200 208 211 376
Riemannain locally symmetric      232 243
Riemannain manifold      I-60 I-154
Riemannain metric      I-27 I-154 I-155
Riemannain symmetric      232 243
Riemannain vector bundle      315
Rigid      45
Rigid affine connection      376
Rigidity      349
Rigidity theorem      43 46 343 353
Scalar curvature      I-294
Schur, theorem of      I-202
Schur, theorem of Kaehlerian analogue of      168
Second fundamental form      13 20
Second fundamental form of a complex hypersurface      175
Sectional curvature      I-202
Sectional curvature, holomorphic      168
Sectional curvature, Kaehlerian      369
Segment      I-168
Semi-simple Lie algebra      325
Simple covering      I-168
Simple Lie algebra      325
Skew-derivation      I-33
Solvable Lie algebra      325
Space form      I-209
Sphere theorem      366
Spherical map of Gauss      9 18 358
Standard horizontal vector field      I-119
Stiefel manifold      6
Strongly curvature homogeneous      357
Strongly curvature preserving      357
Structure constants      I-41
Structure equations      I-77 I-78 I-118 I-120 I-129.
Structure group      I-50
Subbundle      I-53
Submanifold      I-9 1
Submanifold, auto-parallel      53
Submanifold, complex      164 175 378
Submanifold, totally geodesic      I-180 54 234
Symmetric (homogeneous) space      225
Symmetric affine (locally)      222 223
Symmetric complex affine (locally)      259
Symmetric Hermitian (locally)      259
Symmetric Lie algebra      225 238
Symmetric Lie algebra, dual      253
Symmetric Lie algebra, effective      226
Symmetric Lie algebra, irreducible      252
Symmetric Lie algebra, orthogonal      246
Symmetric locally      I-303 222 232
Symmetric Riemannian (locally)      I-302 232 243
Symmetric space      225
Symmetric space, almost effective      225
Symmetric space, effective      225
Symmetric subspace      227
Symmetrization      I-28
Symmetry      I-301 222 225
Symplectic manifold      149
Symplectic manifold, almost      149
Symplectic structure on T*(M)      165
Synge's formula      87
Tangent affine space      I-125
Tangent bundle      I-56
Tangent space      I-5
Tangent space, complex      124
Tangent vector      I-4
Tensor algebra      I-22 I-24
Tensor bundle      I-56
Tensor complex      124
Tensor contravariant      I-20
Tensor covariant      I-20
Tensor field      I-26
Tensor product      I-17
Tensor space      I-20 I-21
Tensorial form      I-75
Tensorial form pseudo-      I-75
Torsion form of an affine connection      I-120
Torsion of an almost complex structure      123
Torsion of two tensor fields of type (1,1)      I-38
Torsion tensor (field) of an affine connection      I-132 I-145
Torsion translation      I-132
Torsion-free connection      332
Torsion-free connection natural      197
Torus      I-62
Torus complex      131 154
Torus Euclidean      I-210
Torus twisted      I-223
Total curvature      362
Total differential      I-6
Total differential of the length function      79
Totally geodesic submanifold      I-180 54
Totally geodesic submanifold of a symmetric space      234 237
Transformation      I-9
Transition functions      I-51
Transvection      236
Trivial fibre bundle      I-51
Twisted cylinder      I-223
Twisted torus      I-223
Type (0, 1), complex vector of      125
Type (1, 0), complex vector of      125
Type ad G      I-77
Type number      42 349
Type of tensor      I-21
Umbilic (umbilical point)      30
Unitary frame      152
Universal factorization property      I-17
Variation of a geodesic      63
Variation of a geodesic, infinitesimal      63
Vector      I-4
Vector bundle      I-113
Vector bundle, orientable, (oriented)      314
Vector bundle, Riemannian      315
Vector field      I-5
Vector field, holomorphic      129
Vertical component      I-63
Vertical subspace      I-63 I-87
Vertical vector      I-63
Volume element      I-281
Weakly irreducible      331
Weil homomorphism      297
Weingarten's formula      15
Weyl group      305
Weyl, theorem of      204 291 330
Whitney sum      306
Whitney sum formula      306 315
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