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Helgason S. — Differential Geometry, Lie Groups and Symmetric Spaces
Helgason S. — Differential Geometry, Lie Groups and Symmetric Spaces

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Название: Differential Geometry, Lie Groups and Symmetric Spaces

Автор: Helgason S.

Аннотация:

The present book is intended as a textbook and reference work on three topics in the title. Together with a volume in progress on "Groups and Geometric Analysis" it supersedes my "Differential Geometry and Symmetric Spaces," published in 1962. Since that time several branches of the subject, particularly the function theory on symmetric spaces, have developed substantially. I felt that an expanded treatment might now be useful


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1978

Количество страниц: 634

Добавлена в каталог: 04.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian Lie algebra      100
Adapted vector field      36
Adjoint group      126
Adjoint operator      143
Adjoint representation      100 127
Adjoint space      327
Affine connection      26
Affine transformation      28
Affine Weyl group      314
Affine, locally symmetric space      198
Almost complex, manifold      352
Almost complex, mapping      355
Almost complex, structure      352
Alpha-series      168
Alternate      13
Alternation      18
Analytic affine connection      36
Analytic diffeomorphism      22
Analytic function      5
Analytic homomorphism      99
Analytic isomorphism      99
Analytic manifold      4
Analytic mapping      2
Analytic pseudo-Riemannian manifold      48
Analytic Riemannian manifold      205
Analytic structure      4
Analytic subgroup      112
Analytic vector field      11
Antipodal set      328
Automorphism inner      127
Automorphism of Dynkin diagram      478 505
Automorphism of root system      421 456
Automorphism of type $(s_0 ,..., s_n ; k)$      510
Automorphism outer      421 478
Ball      51
Basis compatible      264
Basis of a root system      458
Basis of vector fields      10 44
Bergman metric      369
Bi-invariant      135
Bianchi identity      69
Bounded domain      364
Bounded symmetric domain      382
Bruhat decomposition      403
Canonical coordinates      104
Canonical coordinates of the second kind      146
Canonical generators      482
Canonical polynomial      264
Canonical, almost complex structure      355
Cartan decomposition      183
Cartan involution      184
Cartan matrix      459 496
Cartan subalgebra      162
Category theorem      120
Cauchy sequence      55
Cayley transform      95 531
cell      314 321
Center      100 311
centralizer      99 284
Centroid      500
Chain      466
Chain condition      158
Character of a real form      517
Characteristic equation      156
Characteristic polynomial      156
Christoffel symbols      95
Clifford — Wolf isometry      279
Closed form      136
Compact Lie algebra      130
Compact open topology      202
Compact type      230 231
Compactly imbedded subalgebra      130
Complete affine connection      149
Complete Riemannian manifold      55
Completely reducible      192
Completeness at a point      58
Complex 1-form      356
Complex Lie group      392
Complex manifold      4
Complex structure on a Lie algebra      179
Complex structure on a topological space      353
Complex structure on a vector space      178
Complex tangent vectors      357
Complex tensor field      356
Complex vector field      356
Complex vector field, type of      357
Complexification of a Lie algebra      180
Complexification of a vector space      179
Conjugacy      183
Conjugate point      59 294 303
Conjugation      180
Connected      466
Continuation of an isometry      62
Contraction      17
Contravariant      13
Convex neighborhood      34
Convex normal ball      54
Coordinate neighborhood      4
Covariant derivative      42
Covariant differentiation      26
Covariant type      14
Covering group      98
Covering homomorphism      491
covering index      479
Covering Lie algebra      491
Covering manifold      59
Covering of a space      8
Covering space      59
Covering transformation      310
Critical point      279
Curvature      64
Curvature tensor field      44
Curve      28
Curve segment      28
CYCLE      466
de Rham’s Theorem      1
Decomposable      496
Degree of a polynomial mapping      267
Derivation      8
Derivation inner      127
Derived algebra      158
Diagonal matrix      155
Diagram of a compact group      299
Diagram of a symmetric space      295
Diffeomorphism      2 22
Differentiable function      5 30
Differentiable manifold      4
Differentiable mapping      2 22
Differentiable structure      3
Differential      22
Differential form      11
Differential form, bi-invariant      135
Differential form, left invariant      135
Differential form, right invariant      135
Direct product      13
Direct sum      13
Displacement function      278
Dual      11 235
Dynkin diagram      462
Dynkin diagram, extended      505
Effective transformation group      120
Eigenspace      155
Eigenvalue      155
Eigenvector      156
Elliptic      430
Engel’s theorem      160
Exponential mapping      33 104
Expression of a form      20
Expression of a mapping      22
Extendable isometry      62
Exterior differential forms      17
Exterior differentiation      19
Exterior product      19
Flat Riemannian manifold      245
Flat totally geodesic submanifold      245
Free Lie algebra      482
Fundamental group      307 310
Geodesic      29
Geodesic closed, curvature      93
Geodesic manifold      79
Geodesic polar coordinates      95
Geodesic simply closed      327
Geodesic symmetry      198
Gradation      490
Gradation of type $(s_0,..., s_n)$      509
Graph of a mapping      91
Graph of a root system      461
Grassmann algebra      19
Harmonic form      144 227
Height      460
Hermitian matrix      444
Hermitian structure      358
Hermitian symmetric space      372
Holomorphic      4
Holomorphic function      4
Holomorphic mapping      353
Holonomy group      197 193
Homogeneous complex manifold      371
Homogeneous space      120
Homomorphism analytic      99
Homomorphism of a Lie algebra      99
Hyperbolic element      430
Hyperbolic plane      93
Hyperbolic space Hermitian      452
Hyperbolic space quaternian      455
Hyperbolic space real      453
Ideal      99
Ideal, graded      490
Identity component      98
Immediate continuation      62
Imprimitive      151
Indecomposable      496
Indivisible      456
Integrable      353
Integral curve      40
Interior product      40
Invariant, affine connection      28
Invariant, subspace      156
Invariant, tensor field      25
Involution      205 229
Irreducible orthogonal symmetric Lie algebra      377 379
Irreducible pair      377
Irreducible Riemannian globally symmetric space      378
Irreducible root system      458
Irreducible subspace      156
Isometry      60
Isomorphic      109 230 438
Isomorphism      99
Isotropic manifold      535
Isotropy group      121 125
Isotropy subgroup      121
Iwasawa decomposition      260 263 270 273 403 435
Jacobi equation      71
Jacobi identity      9
Jordan decomposition      431
Jordan decomposition, additive      431
Jordan decomposition, complete multiplicative      431
Jordan decomposition, multiplicative      431
Kaehlerian structure      358
Kernel function      367
Killing form      131
Killing form of a root system      523
Laplace — Beltrami operator      92
Left invariant, affine connection      102
Left invariant, differential form      135
Left invariant, vector field      99
length function      315
Lexicographic ordering      173
Lie algebra of a Lie group      99
Lie algebra over a field      99
Lie algebra product      100
Lie derivative      9 89
Lie group      98
Lie subgroup      112
Lie theorem      159
Lie transformation group      121
Lie triple system      224
Lift      59 320
Linear isotropy group      125
Link      466
Link double      466
Link simple      466
Link triple      466
Local chart      4
Local coordinates      4
Local cross section      123
Local isometry      60
Locally finite      8
Locally isomorphic      109
Locally nilpotent      488
Locally, Euclidean      98
Lower triangular      155
Manifold      4
Matrix exponential function      111
Maurer — Cartan equations      137
Maximal compact subgroups      256
Midpoint locus      341
Minimizing ball      54
Mixed tensor algebra      16
Monothetic      287
Multilinear      13
Multiplicity      264 428
Natural topology      120
Negative curvature      72
Nilpotent endomorphism      156
Nilpotent endomorphism, Lie algebra      160
Noncompact type      230 231 252
Normal coordinates      33
Normal coordinates neighborhood      33
Normal coordinates, topological space      8
Normal coordinatesreal form      426
normalizer      99 282 284
One-parameter subgroup      104
Open chart      3
Open chart, submanifold      7
Ordered set      172
Ordered set, vector space      172
Orderings compatible      260
Orientable      361
Oriented      361
Orthogonal symmetric Lie algebra      213
Orthogonal symmetric Lie algebra a pair associated with      213
Orthogonal symmetric Lie algebra, compact type      230
Orthogonal symmetric Lie algebra, decomposition of      231 378
Orthogonal symmetric Lie algebra, duality for      235
Orthogonal symmetric Lie algebra, effective      230
Orthogonal symmetric Lie algebra, isomorphism of      230
Orthogonal symmetric Lie algebra, noncompact type      230
pair      213
Paracompact      8 82
parallel      29
Partition of unity      8
Phi-related      24
Polar coordinate decomposition      402
Polynomial function      267
Polynomial function mapping, degree of      267
Polynomial function, mapping      267
Positive definite      526
primitive      151
Product manifold      7
1 2
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