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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
"Antileibnitz" rule 206 52 53 56 333 488 29 488 424 296 317 33 36 33 a.e. 36 Abelian group 7 Absolute differential 301 371 Absolute integral invariant 263 Accumulation point 13 Active viewpoint 406 Ad G invariant 390 Adjoint map 168 181 Adjoint representation 166 184 Adjoint theorem 63 Admissible atlas 543 Admissible map 368 404 Affine 10 Affine geodesic 302 Affine group 157 Affine parameter 303 Alexandroff theorem 36 Algebra 9 Algebra, Clifford 65 176 416 Algebra, convolution 459 462 Algebra, differential graded 202 Algebra, Dirac 65 Algebra, exterior 196 Algebra, graded 202 Algebra, Grassman 196 Algebra, Lie 134 156 172 Algebra, Pauli 65 Algebra, tensor 140 Algebraic dual 10 Algebraically equivalent 22 Almost complex 331 Almost everywhere 213 Almost hermitian 334 398 Almost kaehlerian 398 Ambrose Singer 381 Analytic manifold 112 Antiderivation 205 Antiselfdual 414 Arc length 320 Arcwise connected 19 Ascoli — Arzela theorem 61 Associated bundle 367 383 Associated Pfaff system 237 Associated space of ideal 233 Associated space Q* 230 Associated topology 20 Associated vector bundle 367 Atiyah — Singer theorem 396 Atlas 111 543 Atlas, admissible 543 Atlas, compatible 543 Atlas, equivalent 112 543 Atlas, examples 186 190 Automorphism 157 174 Auxiliary functions 194 Average formula 501 Baire space 25 Ball 23 Banach algebra 59 Banach manifold 112 543 Banach space 28 Banach theorem 18 Base 14 22 Base (Top, vector space) 21 Base (topological) 14 Base of a bundle 124 Base of neighborhoods 14 Base, orthonormal 31 Basic vector field 378 Basis for 197 Basis in 136 Basis in 134 Basis, Hamel 9 Basis, natural 119 136 Basis, orthonormal 287 Bel — Robinson tensor 340 Betti numbers 224 Bianchi identities 307 309 310 375 Bicharacteristics 252 Bidual (of a Banach space) 59 Bijection 3 Bolzano — Weierstrass theorem 15 Boolean algebra 33 Borel 597 Borel measure 36 Borel sets in R 34 Borsuk's theorem 562 Bound 5 Bound, greatest lower 5 Bound, least upper 5 Bound, lower 5 Bound, upper 5 Boundary 218 222 Boundary-value problems 502 Bounded distributions 525 Bounded linear operator 57 Bounded set 23 Brouwer fixed point theorem 562 Bundle 124 Bundle category 127 Bundle homomorphism 380 Bundle morphism 127 Bundle, cotangent (fibre) 138 545 Bundle, differentiable fibre 127 Bundle, fibre 125 Bundle, frame 129 Bundle, principal fibre 129 Bundle, tangent (fibre) 129 545 Bundle, trivial 125 Bundle, vector 125 C' at x 114 C' differentiable 115 C' mapping 115 C* algebra 59 C*-manifold 112 Calculus of variations 83 Canonical coordinates (one parameter subgroup) 161 184 187 Canonical form 169 Canonical gaussian measure 581 Canonical isomorphism G and 360 Canonical isomorphism on riemannian manifolds 286 Canonical symplectic form 554 Canonical transformation 267 Cardinality 3 Cartan structural equations 306 373 376 Cartan — Killing metric 188 Cartesian product 2 Catastrophe 280 Category 3 Cauchy characteristic manifolds 259 Cauchy net 23 Cauchy problem 256 278 Cauchy sequence 23 25 Cauchy sequence of step maps 51 Cauchy — Kovalevski theorem 493 Cauchy — Schwarz inequality 11 Causal structures 350 Caustics 100 Center (of the group) 7 Chain 217 Characteristic class 390 Characteristic function 1 Characteristic manifold 250 492 Characteristic strips 252 Characteristic system 250 277 Characteristic vector 250 Charge quantization 408 Chart 111 Chem character 393 Chem class 393 Chern number 396 Christoffel symbols 301 308 366 class 79 Clifford algebra 64 176 416 Closed (differential system) 238 Closed form 222 Closed graph theorem 63 Closed map 63 Closed sets 13 Closure 13 Closure (differential system) 238 Cluster point 15 Co variant exterior derivative 372 Co variant spinor 418 Coarser (topology) 12 Cobasis 136 Coboundary 200 222 Cocycle 222 Codimension 10 Coercive (bilinear form) 507 Cohomology 222 Cokernel 401 Collection 1 Commutative group 7 Compact 15 Compact (mapping) 61 564 Compact cohomology 225 Compact support 225 Compact, locally 16 Compact, relatively 16 Compactification 16 Compactified Minkowski space 338 Compatible 543 Complement 2 Complementable split 549 Complementary 9 Complete integrability 243 253 Complete metric space 25 Complete system of exterior equations 232 Complete topological vector space 23 Complete, geodesically 326 Complete, sequentially 23 Completion 25 COMPLEX 397 Complex analytic manifold 112 Complex linear frame 333 Complex measure 49 Complex structure 331 552 Complex, de Rham 399 Complex, elliptic 397 Components of a tangent vector 118 Composite mapping 2 composition 3 Compound matrices 270 Cone property 492 Configuration space 169 265 Configuration space time 265 Conformal automorphisms 350 Conformal group 353 Conformal spaces 350 354 Conjugate points 87 100 344 Conjugate variables 169 Connected 16 Connected, arcwise 19 Connected, locally 17 Connected, locally arcwise 19 Connected, locally simply 19 Connected, simply 19 Connection coefficients 301 Connection forms 301 362 364 371 Connection on a principal fibre bundle 333 357-361 Connection, existence of 308 Connection, linear 300 Connection, metric 300 Connection, Riemannian 308 Conservation of energy theorem 555 Constant mapping 4 Continuous mapping 17 Continuous spectrum 60 Contracted multiplication (tensor) 141 Contracting mapping theorem 88 89 Contraction (tensor) 141 Contravariant functor 4 Contravariant spinor 418 Convergence 15 Convergence (in) 430 Convergence (in) measure 41 Convergence criterion in 454 Convergence in the mean 54 Convergence, strong 29 Convergence, uniform 28 Convergence, weak 30 Convex 10 Convex, locally 22 Convolution algebra 459 462 Convolution of distributions 462 coordinates 111 Coordinates, canonical 161 Coordinates, local 111 Coordinates, local (forms) 197 Coordinates, normal 161 Coset 7 Coset, left 7 Coset, right 7 Cotangent bundle 138 Cotangent space 545 Cotangent vector space 136 Countable 3 Countable set 3 Countable, first 14 Countable, second 14 Countably additive 35 Covariant derivative 301 302 367 370 372 418 Covariant functor 4 Covariant gauge derivative 403 Covariant tensor 546 Covariant vector 545 Covariant vector field 138 Covering 15 Covering space 19 Critical neck theorem 572 Critical point 72 119 546 547 567 Critical value 546 547 567 Cross-section 132 Curl 202 Current 228 484 Curvature 305 306 372 Curvature forms 299 306 372 378 Curvature scalar 310 Curvature tensor 306 Curvature, extrinsic 314 Curve, geometric 262 Curve, integral 144 Curve, parametrized 120 CYCLE 222 620 Cylindrical 576 594 Cylindrical function 578
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