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Michor P.W. — Topics in Differential Geometry
Michor P.W. — Topics in Differential Geometry



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Название: Topics in Differential Geometry

Автор: Michor P.W.

Язык: en

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 317

Добавлена в каталог: 19.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
1-form      73
Adjoint representation      46
Algebraic bracket      135
Algebraic derivation      134
Almost complex structure      142
Anholonomic      17
Associated bundle      158
Atlas      3
Base      12 61
Base space      143
Basis manifold      143
Betti number      88
Bianchi identity      144
Bundle      143
Caley — Hamilton equation      201
Canonical flip      67
Cech cohomology set      62
Center      55
centralizer      55
Characteristic class      194
Chart      3
Charts with boundary      85
Chern character      206
Chern classes      205
Chern — Weil form      194
Chern — Weil homomorphism      194
Christoffel forms      146
Classical complex Lie groups      39
Classifying spaces      163
Closed form      88
Cocurvature      140
Cocycle condition      62 143
Cocycle of transition functions      62 143
Cohomological integral      111
Cohomologous      62 154
Cohomology classes      62
Cohomology group      92
Cohomology of the Lie algebra      130
Compatible      61
complete      20
Complete connection      147
Conjugation      45
Connection      140 144
Connection form, Lie algebra valued      172
Connector      187
Contact of order      209
Cotangent bundle      73
Covariant derivative      187
Covariant exterior derivative      176 189
Curvature      140 188
Curvature form, Lie algebra valued      173
Curve of local diffeomorphisms      24
De Rham cohomology algebra      88
De Rham cohomology algebra with compact supports      99
Degree      119
densities      81
Density or volume of the Riemannian metric      83
Derivation      6
Derivations, graded      134
Diffeomorphic      4
Diffeomorphism      4
Differential      9
Differential form      74
Differential group of order      211
Distinguished chart      29 33
distribution      28 29
Effective action      55
Ehresmann connection      148
Equivalent      3 61
Euler — Poincare characteristic      89
Evolution operator      35
Exact      80
Exponential mapping      43
Exterior derivative      77
f-dependent      141
F-related      21 141
Fiber      61
Fiber bundle      143
Fiber chart      143
Fibered composition of jets      211
Fibered manifold      12
First non-vanishing derivative      24
Flow line      19
Flow prolongation      71
Foliation      31
Frame field      17 64
free      55
Frolicher — Nijenhuis bracket      136
Fundamental vector field      57 58
G-atlas      154
G-bundle      154
G-bundle structure      154
Gauge transformations      166
General linear group      37
Geometric objects      214
Germ of f at x      6
global      20
Graded derivations      134
Graded differential space      91
Grassmann manifold      156
Haar measure      122
Hairy ball theorem      119
Half space      85
Holonomic      17
Holonomic frame field      17
Holonomous      73
Holonomy group      149 179
Holonomy Lie algebra      149
Homogeneous space      56
Homomorphism of G-bundles      161
Homomorphism over $\Phi$ of principal bundles      157
Homotopy operator      90
Horizontal bundle      144
Horizontal differential forms      176
Horizontal foliation      145
Horizontal lift      144
Horizontal projection      144
Horizontal space      140
Horizontal vectors      144
Ideal      54
Idealizer      55
Immersed submanifold      13
Immersion at      12
INDEX      208
Induced connection      183 184
Induced representation      165
Infinitesimal automorphism      31
Initial submanifold      14
Inner automorphism      45
insertion operator      76
Integrable      28 31
Integral curve      19
Integral manifold      30
Integral of the density      81
Invariant of the Lie algebra      193
Invertible      213
Involution      67
Involutive      28 33
Irreducible *-principle connection      180
Jet at      209
k-form      74
k-th order frame bundle      214
Leaf      31
Left action      55
Left invariant      40
Left invariant differential form      121 127
Left logarithmic derivative      47
Lie algebra      18
Lie bracket      18
Lie derivation      135
Lie derivative      22 70 75
Lie group      36
Lie subgroup      52
Linear connection      186 187
Linear frame bundle of      162
Local diffeomorphism      4
Local vector field      17
Long exact cohomology sequence with compact supports      111
Manifold pair      97 111
Manifold with boundary      85
Maurer — Cartan equation      146
Maurer — Cartan form      47
Maximal      30
Natural bilinear concomitants      142
Natural bundles      214
Natural lift      71
Natural transformation      71
Natural vector bundle      68
Nijenhuis tensor      142
Nijenhuis — Richardson bracket      135
normalizer      55
One parameter subgroup      42
Orbit      55
Orientable      84
Orientable double cover      114
Orientations      84
Oriented manifold      84
Orthogonal group      37
Orthonormal frame bundle      163
Orthonormal frame field      163
Pfaffian class      205
Plaque      29 33
Poincare polynomial      89
Pontryagin character      202
Pontryagin classes      197
Pontryagin numbers      199
Principal (fiber) bundle      154
Principal bundle atlas      154
Principal connection      172
Principal fiber bundle homomorphism      157
Principal right action      155
PRODUCT      10
Projection      61 143
Proper homotopy      100
Proper smooth mappings      99
Pullback      145
Pullback vector bundle      65
Pure      3
Quaternionic unitary group      40
Quaternionically linear      40
Quaternionically unitary      40
Reduction of the structure group      157
Relative De Rham cohomology      97
Relative De Rham cohomology with compact supports      111
Representation      45
Restricted holonomy group      149 179
Riemannian metric      162
Right action      55
Right invariant      41
Right logarithmic derivative      46
Right trivialized derivative      123
Section      61
Semidirect product      59
Short exact sequence      92
Signature      118
Singular foliation      31
Smooth distribution      30
Smooth functor      64
Smooth partitions of unity      5
Source mapping      209
Source of a jet      209
spans      29
Special linear group      37
Special orthogonal group      37
Special unitary      39
Sphere      4
Stable      31
Stably equivalent      199
Standard fiber      61 143
Stereographic atlas      4
Stiefel manifold      156
Structure      3
Submanifold      9
Submanifold charts      9
Submersion      12
Support      5 61
Support of a vector field      20
Symplectic group      38
Tangent bundle      8
Tangent space of M at x      7
Tangent vector      6
Target mapping      209
Target of a jet      209
Tensor field      71 73
Time dependent vector field      35
Todd class      207
Topological manifold      3
Total Chern class      205
Total Pontryagin class      197
Total space      12 61 143
Trace classes of a complex vector bundle      206
Trace coefficients      199
Transformation formula for multiple integrals      81
Transition functions      61 143
Transitive action      55
Transversal      15
Truncated composition      210
Typical fiber      61
Unimodular Lie group      122
Unitary      39
Universal vector bundle      169
Vector bundle      61
Vector bundle atlas      61
Vector bundle chart      61
Vector bundle functor      68
Vector bundle homomorphism      64
Vector bundle isomorphism      64
Vector field      17
Vector product      39
Vector subbundle      28 64
Vector valued differential forms      134
Vertical bundle      67 144 170
Vertical lift      67
Vertical projection      67 144
Vertical space      140
Volume      83
Volume bundle      81
Zero section      61
Zero set      5
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