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| Авторизация |
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| Terng Ch. — Critical Point Theory and Submanifold Geometry |
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| Предметный указатель |
 -norm 252
 -invariant deformation 136
-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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