Index
adapted orthonormal frame, 333
adjoint representation, 51
affine action, 66
affine manifold, 298
algebraic Bianchi identity, 302
algebraic bracket, 192
algebraic derivation, 192
almost complex structure, 199
a-pair, 180
angular momentum, 455
angular momentum of a planetary
movement, 428
anholonomic frame field, 22
associated bundle, 215
atlas, 1
base of a fibered manifold, 16
base of a vector bundle, 100
base space of a fiber bundle, 200
basic cohomology, 402
basic forms, 402
basic vector field, 337
basis of a fiber bundle, 200
Betti number, 129
Bianchi identity, 172, 302
Bianchi identity on a fiber bundle, 201
bundle, 200
Cfc-atlas,
1
Cfc-equivalent
atlases, 1
Caley-Hamilton equation, 259
canonical flip, 107
canonical symplectic structure, 417
Cartan moving frame version of a
connection, 232
Cech cohomology set, 101
center of a Lie algebra, 64
center of a Lie group, 64
central extension of a Lie algebra, 170, 463
centralizer in a Lie algebra, 64
centralizer in a Lie group, 64
characteristic class of the invariant
polynomial, 252
chart, 1
charts with boundary, 126
Chern character, 265
Chern classes, 264
Chern-Weil form, 251
Chern-Weil homomorphism, 252
Chevalley cohomology of the Lie algebra,
166
Christoffel forms, 203
Christoffel symbol, 276, 283
classical complex Lie groups, 44
classical second fundamental form, 332
classifying spaces, 220
closed form, 121
coadjoint representation, 421
cocurvature, 197
cocycle condition, 200
cocycle of transition functions, 100, 200
Codazzi-Mainardi equation, 330, 332, 335
cohomological integral, 150
cohomologous, 101, 211
cohomology classes, 101
cohomology group, 132
coisotropic submanifold, 417
coisotropic subspace, 414
compatible, 99
compatible symplectic and complex
structures, 424
complete connection, 204
489
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