Choquet-Bruhat Y., DeWitt-Morette C., Dillard-Bleick M. — Analysis, manifolds and physics. Part I. :: Электронная библиотека попечительского совета мехмата МГУ

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Choquet-Bruhat Y., DeWitt-Morette C., Dillard-Bleick M. — Analysis, manifolds and physics. Part I.

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Название: Analysis, manifolds and physics. Part I.

Авторы: Choquet-Bruhat Y., DeWitt-Morette C., Dillard-Bleick M.

Аннотация:

This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 660

Добавлена в каталог: 03.11.2012

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Предметный указатель

Hyperbolic diagonal      520
Hyperbolic equation      494 511 534
Hyperbolic manifold      287
Hyperbolic operator      521
Hyperbolic structure      293
Ideal      8 232
Ideal, left      8
Ideal, right      8
Identity mapping      3
Image      2
Image of a measure      37 39
Image of a promeasure      578
Image of a vector under a diffeomorphism      134
Image, inverse      2
Image, reciprocal (forms)      138 203 551
Image, reciprocal (function)      115
Immersion      241 549
Implicit function theorem      91
Improper integrals      47
Inclusion theorem      55
Indefinite metric      285 556
INDEX      395 571 572
Index of a quadratic form      287 571
Index, Morse      572
Index, signature      287
Induced measure      46
Induced metric      290 556
Inducting limit topology      427
Inductive topology      18
Infimum      5
Initial integral manifold      257
Injective mapping      2
Inner product      207 285 286 295
Inner product on $A_{x}^{p}$       295
Inner product on $T_{x}(X)$       285
Inner product on $T_{x}^{*}(X)$       286
Instanton      411
Integrability criterion      245
Integrable constraints      247
Integrable function      41
Integrable mapping      51
Integrable Pfaff system      243 244 248
integral      42 214
Integral curve      144
Integral invariant      263
Integral manifold      236 271
Interior      13
Interior product      207 552
Internal operation      6
Intersection      2
Invariant curvature integral      390
Invariant linear differential operator      316
Invariant subgroup      7
Invariant tensor fields      150
Invariant vector fields      155
Invariant with respect to a Pfaff system      261
Inverse derivative of a distribution      450
Inverse function theorem      90
Inverse image      2
Inverse mapping      3
Inverse right translation      154
Invertible      8
Involution      59
Involutive B-algebra      59
Isometry      66 152 298
Isomorphism      4
Isotropic      286
Isovector fields      263
Jacobi equation      87
Jacobi field      87 100
Jacobi identity      134
Jacobian      72
Jacobian matrix      72
Jordan decomposition      49
k-lipschitzian      95
Kahler manifold      330 334
Kahler metric      334
Kernel      10 471
Kernel, Dirac      533
Kernel, elementary      472
Kernel, semiregular      471
Killing forms      168
Killing vector fields      154 298
Kirchoff formula      513
Klein — Gordon equation      589
Kronecker tensor      140
Lagrangian      169
Lagrangian manifold      272
Lagrangian problems      86
Laplace equation      495
Laplacian      318 398 421 440 527
Lattice      5
Least upper bound      5
Lebesgue dominated convergence theorem      43
Lebesgue integral      46
Lebesgue measure      38 39
Left action      163
Left differential      179
Left elementary solution      470
Left invariant form      208
Left invariant vector field      155
Left translation      154
Legendre condition      533
Legendre matrix      102
Leibniz rule      118
Leray form      439
Leray theorem      518 521
Leray theory of hyperbolic equations      516
Leray — Schauder theory      556 565 591
Lie algebra      134 156
Lie algebra isomorphism      165
Lie bracket      134
Lie derivative      134 147 552
Lie group      116
Lie group of transformations      152
Lift      554
Light cone      286
Light rays      535
Limit point      13 15
Line element      293
Linear connection      300 376
Linear continuous responses      530
Linear differential operator      316 485
Linear mapping      10
Linear order      6
Linear vector space      9
Linearly independent      9
Liouville theorem      266 500
Lipschitzian      95
Local chart      543
Local coordinate system      111
Local frame      198
Local gauge      364
Local gauge transformation      402
Local Group      177
Local pseudo group      145
Local transformation      144
Locally arcwise connected      20
Locally compact      19
Locally connected      16
Locally convex      22
Locally finite      15
Locally flat manifold      310
Locally flat space      299
Locally lipschitzian      95
Locally simply connected      19
Loop      386
Lorentz gauge      337
Lorentz group      290
Lorentz group, complete      290

Lorentz group, orthochronous      290
Lorentz group, proper      290
Lorentz rotation      354
Lorentz transformation      66
Losin theorem      41
Lower bound      5
Lowering indices      286
m-almost everywhere      36
Magnetic monopole      408 409
Manifold      111
Manifold (with) boundary      219
Manifold, $C^{k}$       112 543
Manifold, Banach      112
Manifold, causal      350
Manifold, complex analytic      112
Manifold, differentiable      112 543
Manifold, direct product      114
Manifold, E-manifold      543
Manifold, flat, locally flat      310
Manifold, hyperbolic      287
Manifold, orientable      212
Manifold, real analytic      112
Manifold, Riemannian      285
Manifold, time-orientable      288
Manifold, topological      111
Mapping      2
Mapping $C^{r}$       115
Mapping (of) chains      219
Mapping of class $C^{p}$       79 115
Mapping, Cauchy sequence of step      51
Mapping, compact      61 564
Mapping, composite      2
Mapping, continuous      16
Mapping, contracting      88
Mapping, differentiable      71
Mapping, differential      121 546
Mapping, identity      3
Mapping, injective      3
Mapping, integrable      51
Mapping, inverse      3
Mapping, linear      10
Mapping, measurable      40
Mapping, projection      20
Mapping, proper      17
Mapping, sesquilinear      10
Mapping, step      50
Mapping, surjective      3
Matter field      403 404
Maurer — Cartan form      168 364
Maurer — Cartan structure equations      208
Maximal      6
Maximal affine geodesic      302
Maximum theorem      500
Maxwell equations      336
Maxwell stress tensor      338
Mean convergence      54
Mean value theorem      78
Measurable function      40
Measurable map      40
Measure      35
Measure space      35
Measure zero      213
Measure, Borel      36
Measure, completed      36
Measure, complex      49
Measure, Dirac      438
Measure, Haar      39
Measure, image of      37 45
Measure, induced      46
Measure, invariant      37 594
Measure, Lebesgue      38 39
Measure, positive      35
Measure, product      37
Measure, Radon      48
Measure, regular      438
Measure, set      35
Measure, signed      49
Metric      555
Metric connection      381
Metric rescalings      354
Metric space      23
Metric tensor      285
Metric topology      23
Metric transpose      297
Metrizable $\mathscr{P}$ -topology      426
Metrizable space      26
Minimal coupling      403
Minimum      82
Minimum, relative      82
Minimum, strict relative      82
Minkowski inequality      53
Minkowski space      299
Module      8
Moebius band      124
Monge cone      252
Monomial (p-form)      197
monopole      408
Monotone Convergence Theorem      42
Morphism      3
Morphism, bundle      127
Morse      567
Morse lemma      573
Morse theory      567
Moving frame      134
Multiplication (tensors)      140
Natural basis      119 136 197
Natural cobasis      136
Neighborhood      12
Net      15
Neumann problem      503 509
Nondegenerate      11 83 571
Norm      26 58
normal      60
Normal (topological space)      13
Normal coordinate      161 326
Normal subgroup      7
Nowhere dense      13
Null cone      286
Null set      1
Null submanifold      292
Null vector      286
Nullity      571
Numerical function      2
O(N)      166
O-chain      223
O-form      223
Objects      3
Odd forms      212
One parameter group      117
One parameter subgroup      153
One parameter variation      345
One point compactification      16
One-form      138
One-one      3
Onto      3
Open ball      424
Open mapping theorem      63
Open set      12
Operation      6
Operation, external      6
Operation, internal      6
Operators      6
Order (of a) differential equation      492
Order (of a) distribution      437
Order (of a) linear differential operator      485
Order (of a) tensor      139
ordered      6
Ordered, linearly      6
Ordered, totally      6
Ordering      5

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