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Choquet-Bruhat Y., Dewitt-Morette C. — Analysis, manifolds and physics
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Название: Analysis, manifolds and physicsАвторы: Choquet-Bruhat Y., Dewitt-Morette C. 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2Год издания: 1982Количество страниц: 630Добавлена в каталог: 12.01.2014Операции: Положить на полку |
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Предметный указатель
Higgs field 404 Hilbert manifold 112 555 Hilbert space 30 Hilbert — Schmidt operator 62 Hilbert — Schmidt theorem 63 Hilbertian methods 505 507 Hodge decomposition 399 Hodge theorem 400 Hoelder inequality 53 Holonomy bundle 387 Holonomy group 381 387 Hom 3 Homeomorphism 18 Homologous 223 Homology 222 Homology class 223 Homomorphism 7 Homotopic 20 185 Hopf — Rinow theorem 330 Horizontal 358 373 378 Hull 17 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 of a vector field 396 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 3 Inner product 207 285 286 295 Inner product on 286 Inner product on 285 Inner product on 295 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 Iwasawa 386 Jacobi equation 87 Jacobi field 87 100 Jacobi identity 134 Jacobian 72 Jacobian matrix 72 Jordan decomposition 49 k-lipschitzian 95 Kaehler manifold 330 334 Kaehler 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 142 Lagrangian 169 Lagrangian manifold 272 Lagrangian problems 86 Laplace equation 495 Laplacian 318 398 421 449 495 527 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 Lorentzian metric 287 292 Lower bound 5 Lowering indices 286 Lusin theorem 41 m-almost everywhere 36 Magnetic monopole 408 409 Manifold 111 Manifold (with) boundary 219 Manifold, Banach 112 Manifold, C* 112 543 Manifold, causal 350 Manifold, complex analytic 112 Manifold, differentiable 112 543 Manifold, direct product 114 Manifold, E- 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 (of) chains 219 Mapping C' 115 Mapping of class 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 271 336 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 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 134 306 Multi-index 612 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 (hypersurface) 292 315 Normal (topological space) 13 Normal coordinates 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) 175
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