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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