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Terng Ch. — Critical Point Theory and Submanifold Geometry
Terng Ch. — Critical Point Theory and Submanifold Geometry



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Название: Critical Point Theory and Submanifold Geometry

Автор: Terng Ch.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1988

Количество страниц: 271

Добавлена в каталог: 13.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L^p_k$-norm      252
$\pi$-invariant deformation      136
$\pi$-parallel      92
Action integral      233
Adjoint action      74
Affine G-action      73
Affine Weyl group      79
Asymptotic coordinates      43
Asymptotic vector      43
Attaching a handle      204
Backhand transformation      51
Backlund Theorem      51
Basic vector field      90
Best constant      254
Bianchi identity, second      17
Bianchi’s Permutability Theorem      54
Bonnet transformation      62
Bott — Samelson cycle      156 230
Bott — Samelson type      230
Calculus of variations      233
Category      190
Characteristic map      214
Christoffel symbols      244
Closed geodesies      251
Codazzi equations      28
Condition (*)      163
Condition C      181
Condition C modulo G      247
Connection      3
Connection, compatible      8
Contractions      15
Covariant derivative      3
Coxeter graph      82
Coxeter group      79
Coxeter group, crystallographic      81
Critical level      182
Critical point      182
Critical value      182
Curvature distributions      111
Curvature equation      11 26
Curvature normal      111
Curvature normals      70
Curvature of a connection      5
Curvature, constant sectional      12
Curvature, Gaussian      11
Curvature, Ricci      12
Curvature, scalar      12
Curvature, sectional      12
Deformation retraction      213
Distance function      210
distribution      20
Distribution, integrable      20
Dynkin diagram      82
Einstein metric      12
Einstein summation convention      243
Endpoint map of submanifolds      67
Equivariant map      75
Equivariant normal field      86
Euler formula      220
Euler — Lagrange equations      233
Fiber mean curvature vector field      136
First Bianchi identity      11
First fundamental form      25
Flat connection      6
Focal hyperplane      70 113
Focal point      211
Focal point of multiplicity m      69
Focal set      69
Focal submanifolds      162
Focal surfaces      51
Frame field      3
Fredholm action      75
Fredholm map      75
Frenet frame      32
Frobenius theorem      20
Full immersion      112
Fundamental class      229
Fundamental theorem for submanifolds      52
G-action      73
G-invariant partition of unity      78
G-manifold      73
Gauss equations      28
Gauss map      209
Generalized Weyl group      97
Geodesic      33 243
Globally flat      6
Gradient      182
h-projectable submersion      136
Hang up at the level c      223
Harmonic map      248
Height function      210
Hessian bilinear form      197
Hilbert theorem      55
Holder continuous      253
Holomorphic quadratic differential      46
Holonomy group      7
Homotopy spherical complex      216
Horizontal deformation      136
Horizontal lifting      90
Horizontal subbundle      89
Horizontal vector field      90
Immersion      73
Integrable Riemannian submersion      92
Integral submanifold      20
Interior derivative      22
Invariant function      75
Irreducible isoparametric submanifold      79
Isometry      23
Isoparametric map      107
Isoparametric submanifold      102
Isothermal coordinates      43
Isotopy      193
Isotropy representation      85
Lagrangian function      233
Laplacian      16
Laplacian of a tensor      17
Levi — Civita connection      11
Lie derivative      22
Line congruence      51
Line of congruence      51
Line of curvature coordinates      43
Linking type      227
Lipschitz — Killing curvature      150
Lusternik — Schnirelman Theory      189
Maurer — Cartan equation      6
Mean curvature      31
Minimal immersions      31
minimax      188
Minimax principle      188
Minimaxing      186
Morse chart      199
Morse function      197
Morse index theorem      212
Morse inequalities      220
Morse lemma      199
Morse numbers      216
Mountain range      189
Non-critical interval      192
Non-critical neck      192
Non-Critical Neck Principle      194
Non-degenerate      197
Non-focal point      69
Non-linear eigenvalue problem      192 252
Normal bundle, flat      29
Normal connection      26
Normal curvature      28
Normal map of submanifolds      67
Normal slice      85
Orbit space      75
Orbit type      75
Orbit-like submanifold      103
Orthogonal bundle      8
Parallel foliation      131
Parallel section      6
Parallel surface      62
Parallel translation      7
Perfect Morse function      153 221
Polar G-manifold      98
Polar representation      98
Polar variety      63
Positive sectional curvature      12
Principal curvature      31 211
Principal directions      43
Principal horizontal distribution      95
Principal isotropy type      75
Principal orbit      75
Projectable vector field      90
Proper      77
Proper action      77
Protectable deformation      136
Pseudo-spherical congruence      51
Quasi-homogeneous submersion      136
Reflection hyperplane      79
Regular level      182
Regular point      76 182
Regular values      182
Ricci curvature, positivity      12
Ricci equations      28
Riemann tensor      11
Riemannian submersion      89
Root      79
Second fundamental form      26 211
Section      95
Shape operator      25 209
Simple root system      80
Singular point      76
Slice for a G-manifold      76
Slice representation      85
Sobolev Embedding Theorems      254
Sobolev inequality      237
Sobolev spaces      236
Spherical complex      216
Structure equations      11 26
Submersion      89
Taut immersion      152 153
Tchebyshef coordinates      55
Tchebyshef curvature coordinate      54
Tight immersion      150 152
Torsion tensor      9
Total absolute curvature      150
Totally geodesic      33
Totally umbilic      35 37
Tubular neighborhood      85
Umbilic point      43
VBN      239
Vector bundle neighborhood      239
Vector field, Killing      23
Vertical subbundle      89
Vertical vector field      90
Weingarten surface      43
Weyl chamber      80
Weyl group      81
Weyl tensor      14
Yamabe problem      256
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