Электронная библиотека Попечительского совета механико-математического факультета Московского государственного университета   Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум    Авторизация         Поиск по указателям Sternberg Sh. — Lectures on Differential Geometry Обсудите книгу на научном форуме Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter Название: Lectures on Differential Geometry Автор: Sternberg Sh. Язык: Рубрика: Математика/ Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Количество страниц: 390 Добавлена в каталог: 19.11.2008 Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID Предметный указатель Adjoint representation      227 Adjoint system      28 Algebra of contravariant tensors      10 Algebraic preliminaries      1 Almost continuous      113 Ambrose — Singer Theorem      305 Antiderivation      21 102 Antisymmetric tensors      14 Approximation theorems      55 ARC      207 Associated bundle      307 Associated system      24 Barycentric coordinates      104 105 Bases      8 Betti numbers      289 Bi-invariant Riemann metric      232 Bianchi — Cartan identities      330 Bianchj's identities      360 Bilinear map      2 binomial      253 Bonnet's theorem      292 Buler vector field      159 Bundle of frames      80 Bundle of orthonormai frames      247 Calculus of variations      148 Cartan's Lemma      18 Cellulated surface      288 Characteristic system      135 Classical mechanics      141 Closed differential form      108 Closed subgroups      228 Closed submanifold      43 Cohomology group      108 Complete Riemannian manifold      173 Complete spray      199 Completely integrable      130 Completeness      207 Conjugate points      182 Connection form      298 Connection on a principal bundle      298 Connection on an associated bundle      308 Connections      294 Conservation laws      170 Conservation of energy      146 Content      113 Content zero      113 Contraction of tensors      6 Contravariant and symmetric algebras      10 Contravariant degree      6 Contravariant vector field      79 Coordinate chart      35 Coordinate map      34 Coordinate neighborhood      34 Coordinates of die chart      36 Cotangent bundle      79 Covariant degree      6 Covariant derivative, with respect to a linear connection      352 Covariant derivative, with respect to a parallelism      341 Covariant differential      355 Covariant vector field      79 Critical points      47 Critical value      47 Cross section      295 Curvature of a connection      300 Curvature of a ribbon      253 Curves in Euclidean space      252 Darboux's theorem      137 141 Decomposable p-vectors      19 Degree of a map      120 densities      111 112 Derivation      102 Diffeomorphism      43 Differentiable function      45 Differentiable manifolds      31 35 Differentiable p-chains      106 Differential form of degree p      82 Differential system      130 Energy of a Lagrangian      152 Equations of structure of Euclidean space      237 238 Equations of structure, of a Riemann manifold      246 249 Equations of structure, of a submanifold      245 Equations of structure, of a submanifold of Euclidean space      251 Euler — PoincarЈ characteristic      290 Euler's differential equation      159 166 Exact differential form      108 Exponential map      222 Exterior 2-fornis      23 Exterior algebra      14. 15 Exterior differential form of degree p      82 Exterior differentiation      100 Exterior equations      23 Exterior forms      20 Exterior multiplication      20 Extremal      167 F-related      95 Field of quantities      78 Flat G-structure      315 Focal point      18 frames      8 Frenet equations      253 Frenet ribbon      253 Frenet trihedral      253 Frobenius' Theorem      130 Fundamental form      143 G-connection      352 G-structures      293 310 Gauss' lemma      201 Gaussian curvature      266 General equivalence problem      314 Geodesic flow on T(M)      199 Geodesic spray      200 Geodesies of a Riemann metric      167 Hamilton — Jacobi equation      179 Hamiltonian manifold      141 Hamiltonian structures      141 Hamiltonian vector field      143 Higher order structures      337 Holonomy group      300 301 Homogeneous ideal      26 Homomorphism of principal bundle      294 Horizontal vector field      299 Imbedding      42 Immersed submanifold      43 Immersion      42 Indefinite metric      13 Inner product      22 Integral calculus on manifolds      97 Integral manifold      130 Interior multiplication      20 Invariant metrics      231 Isometries      212 Isomorphism of principal bundles      294 Jacobi equations      186 Jacobi vector field      185 Jacobi's condition      182 Jacobi's identity      94 222 kinetic energy      149 Knbayashi's theorem      347 Left invariant forms      217 Left invariant spray      222 Left invariant vector fields      218 Legendre transformations      150 Lensor algebra of a vector space      5 Levi — Civita's theorem      334 Lie algebra      94 217 218 Lie bracket      94 Lie derivatives      89 91 Lie groups      214 Lie homomorphism      216 Lie subgroups      216 Linear connection      352 Linear differential form      79 Linear map      2 Linear quantity      10 Liouville form      171 Locally bounded      112 Lorentzian metric      14 Maurer — Cartan equation      218 Maximal integral manifold      136 Moving frames      244 Multilinear map      3 Necessary conditions for a minimum      153 Non-singular metric      13 Normal coordinates      222 One parameter group      89 Operator D      99 Orientable      115 Orientation on a manifold      116 Oriented manifold      116 Orthogonal frames      240 Partitions of unity      55 57 Path      207 Poincare's lemma      121 Poisson bracket      142 Positive definite Lagrangian      176 Principal bundles      73 294 Principal normal      253 Prolongations of       331 Prolongations of a G-structure      331 Proper imbedding      43 Proper map      43 quantities      73 76 Rank of a collection of functions      341 Ray      208 Regular family of functions      342 Regular Lagrangian      152 Restricted equivalence problem      339 ribbon      252 Right interior multiplication      22 Sard's theorem      45 Scalar densities      10 Scalar product      22 Second fundamental form      264 Second order differential equation      166 Second order structures      337 Segment      207 Singulars-simplex      106 Space of exterior p-forms over V      20 Space of m-frames of V      36 Space of symmetric tensors      12 Spherical map      264 Spray      199 Spray of a linear connection      361 Stokes' theorem      109 119 Structure function of a G-structure      318 Structure group of a bundle      294 Sturm's theorem      291 Submanifold      43 Sufficient conditions in the calculus of variations      174 Support of a density      112 Support of a form      109 Surfaces      279 Symmetric bilinear forms      13 Symmetric tensors      14 Tangent space      69 70 Tangent vector      69 Tensor bundles      84 Tensor field      80 Tensor products of vector spaces      2 4 5 Theorem Egregium      267 Thorn's transversality theorem      65 Topological group      231 Torsion of a curve      253 Torsion of a linear connection      356 Torsion of a ribbon      253 Total angular momenta      147 Total linear momenta      147 Transitive G-structures      321 Trivial bundle      295 Twist of a ribbon      253 Universal property      1C Vector fields      89 Vector product      23 Vector space      2 Vector valued forms      234 Реклама        © Электронная библиотека попечительского совета мехмата МГУ, 2004-2024 | | О проекте