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