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Spivak M. — A Comprehensive Introduction to Differential Geometry (Vol.1)

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Название: A Comprehensive Introduction to Differential Geometry (Vol.1)

Автор: Spivak M.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: third edition

Год издания: 1999

Количество страниц: 489

Добавлена в каталог: 06.04.2007

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

Предметный указатель

-related      190
$\sigma$ -compact      4 459
${C}^{0}$ manifold      34
${C}^{\infty}$ distribution      179
${C}^{\infty}$ form      207
${C}^{\infty}$ function      32
${C}^{\infty}$ manifold      29
${C}^{\infty}$ manifold-with-boundary      32
${C}^{\infty}$ Riemannian metric      308
${C}^{\infty}$ structure on TM      82
${C}^{\infty}$ -related      28
Abelian Lie algebra      376 382 395
Adams, J.F.      100
Adjoint T* of a linear transformation T      103
Ado, I.D.      380
Alexander's Horned Sphere      55
Algebra. Fundamental Theorem of      285 293
Algebraic inequalities, principle of irrelevance of      233
Alternating, covariant tensor field      207
Alternating, multilinear function      201
Alternation      202
Analytic manifold      34
Annihilator      228
Annulus      8
Antipodal, map      278
Antipodal, point      10
Arclength      312
Arclength, function      313 332
Arcwise connected      20
Arcwise, subgroup of a Lie group      409
Area, generalized      246
Associated, disc bundle      451
Associated, sphere bundle      451
Atlas      28
Atlas, maximal      29
Auslander, L.      106
Banach space      145
Base space      71
Basis, dual      107
Basis, for ${M}_{p}^{*}$       208
Basis, for ${\Sigma}^{k}(p)$       208
Belongs to a distribution      191
Besicovitch, A.S.      179
Bi-invariant metric      401
Big, disc      466
Big, half-plane      466
Big, plane      466
Big, quadrant      466
Boundary      19 248 252
Bounded manifold      19
Boy's Surface      60
Bracket      154
Bracket, in $gl(n, \mathbb{R})$       378
Bracket, in $o(n, \mathbb{R})$       379
Bundle, cotangent      109
Bundle, dual      108
Bundle, fibre      309
Bundle, induced      101
Bundle, map      73
Bundle, n-plane      71
Bundle, normal      344
Bundle, of contravariant tensors      120
Bundle, of covariant tensors      117
Bundle, tangent      77
Bundle, trivial      72 210
Bundle, vector      71
Burali — Forti paradox      464
C' manifold      34
Calabi, E.      472
Calculus of variations      316
Cartan's Lemma      230
Cartan, Elie      39 348 360
Cauchy — Riemann equations      200
Cayley numbers      100
Chain      248 285
Chain rule      35 38
Chan      28
Change, infinitely small      111
Choice      283
Choice function      467
circle      6
Closed, form      218 252
Closed, geodesic      367
Closed, half-space      19
Closed, long ray      465
Closed, manifold      19
Closed, subgroup of a Lie group      391
Closed, submanifold      49
Closed, up to first order      160
Cofinal      465
Cohomology      419
Cohomology, de Rham      263
Cohomology, group of M with real coefficients      263
Cohomology, of a complex      421
Commutative diagram      65 420
Commutative Lie algebra      310
Complete, geodesically      341
COMPLEX      421
Complex, analytic structure      470
Complex, numbers of norm 1      373
conjugate      358
Constants of structure      396
Continuous homomorphism      387
Contractible      220 225 236
Contraction      121 139 227
Contraction, lemma      139
Contravariant, functor      130
Contravariant, tensor field      120
Contravariant, vector field      113
Convex, geodesically      363
Convex, polyhedron      429
Coordinate lines      159
Coordinate system      28 158
coordinates      28
Cotangent bundle      109
Covariant functor      130
Covariant icnsor field      117
Covariant vector field      113
Cover, locally finite      50
Cover, point-finite      60
Cover, refinement of      50
Cramer's rule      372
Critical point      40
Critical point in the calculus of variations      320
Critical value      40
Cross section      227
Cross-cap      14
Cross-product      299
Cube, singular      246
Cup product      299 439
Curl      238
Cylinder      8
Darboux integrable      283
Darboux integral      283
Darboux's theorem      284
de Rham cohomology vector spaces      263
de Rham cohomology vector spaces, with compact supports      268
de Rham's theorem      263 457
de Rham, G      342
Debauch of indices      39 123
Decomposable      228
Definition, invariant      214
Deformation retraction      279
Degenerate      286
Degree      275
Degree, mod 2      295
Density, even scalar      133 209
Density, odd scalar      133 259
Density, relative scalar      231
Density, scalar      133

Derivation      39 78
Derivation, of a ring      83
Derived set      25
Descartes — Euler theorem      429
Determinant      232
Diffeomorphic      30
Diffeomorphism      30
Diffeomorphism, one-parameter group of      148
Differential      210
Differential, equation      136 164
Differential, equation, depending on parameters      169
Differential, equation, linear      165
Differential, forms      201
Differential, of a function      109
Difierentiable      27 28 31 32
Difierentiable, at a point      31
Difierentiable, manifold      29
Difierentiable, structure      30
Difierentiable, structure, on $\mathbb{P}^{n}$       32
Difierentiable, structure, on $\mathbb{R}^{n}$       29
Difierentiable, structure, on ${S}^{n}$       30
Difierentiable, structure, on the long line      471
DIMENSION      4
Direct sum      421
Disc bundle, associated      451
Discriminant      233
Disjoint union      4 20
distribution      179 181
Distribution, ideal of      215
Distribution, on torus      180
Divergence      238
Divergence, Theorem      352
Domain      3
Du Bois Reymond's Lemma      355
Dual, basis      107
Dual, space      107
Dual, vector bundle      108
Einstein summation convention      39
Elements of norm 1      308
Elliptical non-Euclidean geometry      367
Embedding      49
END      23
End, paracompact      468
Endomorphism      121
Energy      324
Envelope      358
Equations depending on parameters      169
Equations of structure      404
Equivalence (of vector bundles)      72
Equivalence, weak      96
Euclidean, metric      305 315
Euclidean, motion      374
Euclidean, n-space      1
Euler      429
Euler's equation      320
Euler, characteristic      428
Euler, class      445
Even, ordinal      467
Even, relative scalar      231
Even, relative tensor      134 231
Even, scalar density      133 209
Exact form      21—8
Exact sequence      419 422
Exact sequence, of a pair      433
Exact sequence, of vector bundles      103
Exponential map      334 385
Exponential of matrices      384
Extension      432
Extremal      320
Faith, leap of      464
Fibre      64 68 71
Finite characteristic      205
Finite type      438
first element      461
First variation      319 327
Five lemma      440
Fixed point      139
Foliation      194
Folium      194
Force field      240
FORM      207
Form, differential      201
Form, left invariant      374
Form, right invariant      400
Frobenius Integrabilitv Theorem      192 215
Fubini's theorem      254
functor      130
Functorites      89
Fundamental theorem of algebra      285 293
Fundamental theorem of calculus      254
Gauss's lemma      337
General linear group      61 372
Generalized area      246
Geodesic      333
Geodesic, closed      367
Geodesic, reversing map      401
Geodesicallv convex      363
Geodesically complete      341
Geodesy      333
Germs of k-forms      432
Global theorv of integral manifolds      194
Gradient      237
Grak      84
Gram — Schmidt orthonormalization process      304
Group, Lie      371
Group, matrix      372
Group, opposite      407
Group, orthogonal      372
Group, topological      371
Guillemin, V.W.      106
Hahn — Banach theorem      145
Hair      69
Half-long cylinder      466
Half-long line      465
Half-long strip      466
Half-space      19
Handle      8
Hardy, G.H.      179
Has one end      23
Hausdorff      459
Heinlcin, Robert A.      84
Homogeneous      7
Homomorphism, continuous      387
Homomorphism, of Lie algebras      380
Homotopic      104 277
Homotopy      104 277
Hopf — Rinow — de Rham Theorem      342
Hopf, H.      342 450
Hyperbolic, cosine      356
Hyperbolic, sine      356
Hyperbolic, tangent      356
Ideal of a Lie algebra      410
Identification      10
Imbedding      49
Imbedding, topological      14
Immersed submanifold      47
Immersion      46
Implicit function theorem      60
Indefinite metric      350
Independent infinitesimals      314
Index of inner product      349
Index of vector field on $\mathbb{R}^{n}$       446
Index of vector field on a manifold      447
Indices, debauch of      39 123
Indices, raising and lowering      351
Induced, bundle      101
Induced, orientation      260
Inequalities, principle of irrelevance of algebraic      233
Inertia, Sylvester's law of      349
Infinite volume      312

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