Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Sharpe R.W. — Differential Geometry: Cartan's Generalization of Klein's Erlangen Program
Sharpe R.W. — Differential Geometry: Cartan's Generalization of Klein's Erlangen Program

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Differential Geometry: Cartan's Generalization of Klein's Erlangen Program

Автор: Sharpe R.W.

Аннотация:

Cartan geometries were the first examples of connections on a principal bundle. They seem to be almost unknown these days, in spite of the great beauty and conceptual power they confer on geometry. The aim of the present book is to fill the gap in the literature on differential geometry by the missing notion of Cartan connections. Although the author had in mind a book accessible to graduate students, potential readers would also include working differential geometers who would like to know more about what Cartan did, which was to give a notion of "espaces g?n?ralis?s" (= Cartan geometries) generalizing homogeneous spaces (= Klein geometries) in the same way that Riemannian geometry generalizes Euclidean geometry. In addition, physicists will be interested to see the fully satisfying way in which their gauge theory can be truly regarded as geometry.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 220

Добавлена в каталог: 23.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Action, effective      138
Action, free      145
Action, proper      145
Action, transitive      138
Ado's Theorem      127
Affine coordinate system      5
Affine plane      141
Atlas      5
Atlas, Cartan      174
Atlas, q-codimensional foliated      82
Bianchi identities, first and second      193 236
Bianchi submodule      232
Bundle      29
Bundle, automorphism      30
Bundle, base space      29
Bundle, construction of G bundles      35
Bundle, effective G bundle      31
Bundle, exterior power      38
Bundle, flat      32
Bundle, G atlas      31
Bundle, G bundle      31 32
Bundle, G structure      32 33
Bundle, induced or pullback bundles      32
Bundle, isomorphic G bundles      33
Bundle, isomorphism      30
Bundle, principal      36 37
Bundle, product bundle      32
Bundle, quotient bundle      38
Bundle, reduction      147
Bundle, section      38
Bundle, smooth      29
Bundle, tangent      46
Bundle, total space      29
Bundle, transition function      31
Bundle, trivial or product      30
Bundle, trivialization      30
Bundle, vector bundles      37
Bundle, Whitney sum      38
Calculus, fundamental theorem      66
Canonical line bundle      31 268
Cart an connection      181
Cartan atlas      174
Cartan gauge      174
Cartan geometry      176 184
Cartan geometry of $\mathfrak{g}$-curvature type V      201
Cartan geometry of curvature type V      201
Cartan geometry, admissible frames      191
Cartan geometry, Bianchi identity      192 193
Cartan geometry, connection      181
Cartan geometry, constant curvature      221
Cartan geometry, covariant derivative      198
Cartan geometry, curvature      184
Cartan geometry, curvature function      191
Cartan geometry, curvature section      192
Cartan geometry, effective      176 184
Cartan geometry, first-order      191
Cartan geometry, flat      177
Cartan geometry, generalized circle      210
Cartan geometry, geometric orientation      203 207
Cartan geometry, geometrically oriented      207
Cartan geometry, higher-order      191
Cartan geometry, holonomy      210
Cartan geometry, isomorphism      176 185
Cartan geometry, local isomorphism      185
Cartan geometry, locally symmetric      225
Cartan geometry, moduli space of      217
Cartan geometry, normal      202
Cartan geometry, primitive      184
Cartan geometry, reductive      184 197
Cartan geometry, space form      221
Cartan geometry, special curvature      201
Cartan geometry, tangent bundle of      188
Cartan geometry, tensors of type $(V, \rho)$      194
Cartan geometry, torsion      184
Cartan geometry, torsion free      184
Cartan structure      176
Cartan's formula      263
Cauchy — Riemann operator      403
Charts      5
Charts, compatible      6
Charts, compatible along a path      7
Clebsch — Gordan problem      398
Collinear points in $P^{n}$      332 337
Complete, 1-form      129
Complete, vector field      69
Complex projective line      144
Conformal, arclength      320
Conformal, curvature      320
Conformal, metric      277
Conformal, transformation      271
Conformally flat      236
Constant curvature      236
Constant of integration      115
Contact elements      354
Covariant constant      198
Covariant derivative      371
Covariant derivative, base version      199
Covariant derivative, universal      194
CR geometry      355
Curl      404
Curvature      176
Darboux derivative      115
Derivation      50
Derivation at p      42
Development      368 377
Development of a $\mathfrak{g}$-valued 1-form      119 120
Diffeomorphism      11
Differential equation      331 354
Differential form, 1-form      52
Differential form, basic and semibasic      62
Differential form, p-forms      54
Differential form, transforming according to a representation      195
Differential operators      195
Dirac operator      405
Directional derivative in $R^{n}$      42
distribution      74
Distribution, associated to a foliation      82
Distribution, integral submanifold      75
Distribution, involutive or integrable      74
Distribution, local basis      74
Divergence      404
Dual principal curvature      256
Ehresmann connection      235 358
Ehresmann connection, curvature of      358
Einstein manifold      236
Elliptic curve      24
Elliptic plane      141
Embedding      16
Embedding, weak      17
Equivalence problem for conformal metrics      285
Equivalence problem for Weyl structure      292
Euclidean geometry      227 234
Euclidean group      228
Euclidean model      228
Euclidean n-space      242
Euclidean plane      140
Exterior derivative of a function      52
Exterior derivative of a p-form      56
Exterior product of p-forms      55
Families of submanifolds      354
Fiber      29
Flow generated by a vector field      73
Foliation      82
Foliation, characterization of simple      90
Foliation, leaf      82
Foliation, production or trivial      83
Foliation, simple      90
Foliation, vertical foliation of a bundle      83
Frame bundle, fundamental forms      363
Frobenius theorem      76
Frobenius theorem, theorem, differential form version      81
Fundamental theorem of calculus      124
Gauge      165
Gauge symmetry      169 178
Generalized circle      337
Geodesics      236 344
Geodesics, configuration of      352
Geometric rigidity      216
Geometry of similarity      141
Grassmannian      147
Group of periods      122
Holonomy group      210
Holonomy group, restricted      211
Holonomy of a leaf      86
Holonomy, Cartan      210
Holonomy, Ehresmann      369
Homogeneous space      153
Homomorphism      13
Hopf fibration      33
Horizontal, curve      368
Horizontal, distribution      198
Horizontal, vector      269 368
Hyperbolic n-space      242
Hyperbolic plane      140
Infinitesimal gauge      167
Integral of $\mathfrak{g}$ valued 1-form      115
Involutes of curves      359
Isoparametric      259
Jacobian variety      136
Klein geometry      151
Klein geometry, associated effective      151
Klein geometry, effective      151
Klein geometry, first order      164
Klein geometry, fundamental property      160
Klein geometry, geometric isomorphism      153
Klein geometry, geometrically oriented      151
Klein geometry, higher order      164
Klein geometry, infinitesimal      156
Klein geometry, kernel      151
Klein geometry, Lie theoretic properties      153
Klein geometry, locally effective      151
Klein geometry, one-dimensional effective geometries      157
Klein geometry, primitive      151
Klein geometry, principal group      151
Klein geometry, space      151
Klein geometry, tangent bundle      163
Klein pair      156
Klein pair, effective      156
Klein pair, reductive      156
Klein space      153
Leaves, space of      90
Levi-Civita, connection      235 358
Levi-Civita, parallelism      362
Lie algebra      103
Lie algebra, representation      127
Lie algebra, subalgebra and ideal      103
Lie group      12
Lie group, adjoint action and representation      110
Lie group, characterization      130
Lie group, completeness of left-invariant fields of      106
Lie group, left and right translation      96
Lie group, left invariant field $v^{\dagger}$      102
Lie group, left invariant vector fields      101
Lie group, Lie group-Lie algebra correspondence      107 126
Lie group, one-dimensional subgroups      105
Lie group, product and quotient rules      113
Lie group, standard examples      63
Lie group, structural equation      108
Lie group, vector field $X^{\dagger}$ induced by action of      107
Lie sphere plane      143
Light cone      142
Lightlike, subspace      268
Lightlike, vector      268
Line in $P^{n}$      337
Locally ambient geometry      247
Locally Klein geometry      154
Locally, flat      18
Lorentz plane      141
Manifold, G structure      48
Manifold, immersed      26
Manifold, orient able      6
Manifold, reduction of structure group      48
Manifold, smooth      6
Manifold, topological      3
Manifold, topological orientation      7
Maurer — Cartan form      98
Mean curvature vector      256
Method of equivalence      331
Model algebra, Moebius geometry      271
Model algebra, Moebius subgeometry      295
Model algebra, projective geometry      332 338
Model algebra, Riemannian geometry      228
Model algebra, Riemannian subgeometry      245
Model geometry      174
Model geometry, effective      174
Model geometry, kernel      174
Model geometry, primitive      174
Model geometry, reductive      174
Moduli space of Cartan geometries      217
Moebius band      30
Moebius geometry      277
Moebius geometry, locally ambient      305
Moebius geometry, normal      280
Moebius geometry, normal submodule      275
Moebius geometry, Ricci homomorphism      275
Moebius geometry, special curvature      278
Moebius geometry, three-dimensional normal      281
Moebius group      269
Moebius model      269
Moebius model, Lie algebra for      272
Moebius plane      142
monodromy      122
Monodromy and covering transformations      128
Monodromy group      122
Monodromy representation      122
Mutation      154 217 243
n-sphere      3 5 24 242 273
No-slip condition      377
no-twist condition      377
Normal bundle      247 248 305
Normal bundle, relatively flat      254
Normal submodule      202 275 336
One-parameter groups      71 72
parallel      198
Period group      122
Period group, defined up to conjugacy      122
Period map      115
Period map, classical      136
Plaque      18
Plaque, chart      18
Plethysm      397
Poincare, first return map      86
Primitive models      218
Principal bundle      36 37
Principal bundle, reduction      147
Principal curvature decomposition      256
Principal curvatures      253
Principal curvatures, constant      259
Principal subspaces      256
Projective completion      143
Projective geometry      338
Projective geometry, curvature function      340
Projective geometry, normal      342
Projective geometry, normal space      353
Projective geometry, special geometries      341
Projective geometry, subgeometry      353
Projective geometry, symmetric      342
Projective geometry, torsion free      339
Projective group      334
Projective model      334
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте