|
|
 |
| Àâòîðèçàöèÿ |
|
|
|
| Ïîèñê ïî óêàçàòåëÿì |
|
|
|
|
|
|
|
 |
|
|
|
| Bryant R., Griffiths P., Grossman D. — Exterior differential systems and Euler-Lagrange PDEs |
|
|
|
| Ïðåäìåòíûé óêàçàòåëü |
Admissible lifting 156—161 165
Affine frame bundle 58—65
Affine fundamental forms 59—65 73
Affine hypersurface 37 57—65 73 74
Affine normal line 60—63
Affine transformation x 58—65
Area functional vii 15 24—35
Asymptotic curve 184 190
Backlund transformation xi 23 188 190—197
Basic form xii 57
Betounes form xi 158—164
Bianchi identity 91—92
Bianchi, L. 193
Blaschke, W. 61
Calibration 145—149 156
Cartan lemma 24 59 60 94 108
Cartan, E. ix xi 37
Cauchy problem 118—120
Cauchy — Schwarz inequality 129
Characteristic cohomology 4
Characteristic system 183—185
Christodoulou, D. 118
Coframe bundle 38
Conformal bundle 104
Conformal curvature 82
Conformal energy 127
Conformal flat model 79—85 91 96—100 102 115—118
Conformal frame bundle 83 85
Conformal group 40 79 97 101 111 139
Conformal inner-product 80 83 136
Conformal Laplacian 79 80 93—97 102 120 138
Conformal structure x 79—110 133 136—140 149
Connection 42 52
Connection, Cartan 85 91 137
Connection, Levi — Civita 22 77 87 95 141 142
Conservation law ix 14—21 79
Conservation law for  123—127
Conservation law for  110—118
Conservation law for cmc hypersurfaces 32—34
Conservation law for harmonic maps 166—168
Conservation law for K = -1 surfaces 183—190
Conservation law for minimal hypersurfaces 27—32
Conservation law for wave equations 118—127
Conservation law, higher-order 176—190
Conservation law, proper 15 18—19
Conservation law, trivial 15 116 188
Conservation law, “almost” 34—35 125
Conservation law, “hidden” 31
Contact, form 2 7 15 16 98 102 103 124
Contact, ideal 3 4 10
Contact, line bundle 4 10 16 52 123 125
Contact, manifold ix 1—8 10 39 77 83 97
Cotten tensor 92
Covariant derivative 90 92 94 95 109 138—144 165
Darboux theorem 50
Decomposable form 41 53 183
Density line bundle 92—97 124 126 138 149
Dilation 34 84 116 121 123
Divergence equivalence 155 156
Energy vii 122—123 127—129
Energy of a map 164 165
Equivalence method ix 37—38 41—53 65—74 79 85—88 102—110 134
Equivalence of conformal structures 85—92
Equivalence of G-structures 42
Equivalence of Lagrangians 3
Equivalence of Monge — Ampere systems 39— 52
Equivalence of Poincare — Cartan forms 65—78 102—110
Euclidean frame bundle 21 26 28 182
Euclidean motion 21—34 78
Euclidean space vii 21—35
Euler — Lagrange equation vii viii 7 10 72 99 151 156
Euler — Lagrange system ix 1 7—15 40 51 133—149
Exterior differential system xii
Field 147—150
First variation viii 7 133—134
Frobenius theorem 55
Functional vii—ix 3—7
G-structure 37—38 41—50 85—88 102
Gauss curvature 13 41 182—197
Gauss map 23
Generating function 16—17
Grassi, M. 155n 163n
Grassmannian 2 13 56 142 151
Green’s Theorem viii 127—130
Harmonic function 29
Harmonic map xi 164—168
Hodge — Lepage decomposition 4
Holder’s Inequality 130
Holomorphic curve 31—32
Ideal, algebraic 2n 154
Ideal, differential 2 9 10 158
Independence condition 2 20
Integrable extension xi 185—188
Integral manifold xii 2 4 15
Integral manifold, transverse 12
Inverse problem 1 7 10—14 24 39 51
inversion 84 117 121 125
Jacobi operator ix 145 149—150
Jets vii 2 99—100 103
John, F. 129
K3 surface 13
Killing vector fields 166
Koszul complex 144
Lagrangian vii—ix 3—7 155—164
Lagrangian potential 57—58 73 145
Laplace equation 139
| Legendre submanifold 2—3 7—11 133—145 158
Legendre submanifold, non-transverse 23 27 196
Legendre submanifold, transverse 3 9 142
Legendre variation 7—9 134—149
Levine, H. 128n
Lorentz boost 121
Lorentz, conformal group 119 121 126
Lorentz, frame 81 83 98
Lorentz, metric 78 119
Lorentz, space 80
Maurer — Cartan equation 58 82
Maurer — Cartan form 80—82 85 100 167
Mean curvature vii 13 24
Mean curvature, constant 24 27 141
Mean curvature, prescribed x xi 38 74 77 105n 133 140—145
Minimal surface ix 15 24—35 78 145
Minkowski space 20 118—127
Minkowski space, compactified 119
Moment conditions 31—34
Monge — Ampere system 10—14 99
Monge — Ampere system, hyperbolic ix 40—52 182
Moving frames 59
Multi-contact geometry 151—158
Noether’s theorem ix 1 7 10 14—21 28 29 79 114 115 163 184
Non-degenerate, 1-form 1
Non-degenerate, affine hypersurface 59—60
Non-degenerate, functional 9 10 15
Null vector 80
Null vector, positive 80 97
Pfaff theorem 2 154
Pfaffian system xii
Plateau problem 31
Poho?zaev’s theorem 117
Poincar?e lemma 11 50 55
Poincare — Cartan form ix 1 6—11 133—147 151—164
Poincare — Cartan form, almost-classical 52—56 65—67
Poincare — Cartan form, conformally invariant 97—118
Poincare — Cartan form, definite 67—74 102—110 135
Poincare — Cartan form, Euclidean-invariant 25—26
Poincare — Cartan form, neo-classical x 37 52—59 65—67 74—78 98
Poisson equation x 11—13 79
Poisson equation, conformally invariant 110—118
Poisson equation, non-linear 96—97 102—110 118 188
primitive 4 9n 10—12 39—40
Principal direction 183
Prolongation of a G-structure x 42 85—88
Prolongation of a linear Lie algebra 87
Prolongation of an EDS 183
Pseudo-connection 42—52 85—90 103
Pseudosphere 23
Pseudospherical line congruence 192—195
Ricci curvature 95
Riemann curvature tensor 22 78 89 105 137 142
Riemannian frame bundle 22 77 95 141—144 164
Riemannian Laplacian 96 144
Riemannian manifold 22 74 87
Riemannian metric 77—78 80 95 140
Rotation 29 34 84 116
Rumin, M. 9n
Scalar curvature 95 106
Second fundamental form 24 26 141 183
Second fundamental form of a map 166
Second variation ix x 78 133—140
Second variation for prescribed mean curvature 140—145
Semibasic form xii 38 43 57
Simple foliation 56 78n 97 104
Sine-Gordon equation xi 185—188 190—195
Space-like hypersurface 78
Spencer cohomology 44 87
Stationary vii—ix 7—10 134—149
Stereographic projection 79 119
Stokes’ Theorem 147—148
Strauss, W. 121n
Stress-energy tensor 166
Strong local minimum 145—149
Summation convention 68
Symbol 10 162
Symmetric form 159 165
Symmetry ix 14—21 78—85 102 111—113 136
Symmetry, generalized 188
Symmetry, hidden 188
Symplectic linear algebra 4—6 10 11 17—18 50 164
Symplectic transformation 39—40
Tautological 1-form 38 42—50 85
Time-orientation 80
Torsion of a pseudo-connection 43—52 85—90 103
Torsion, absorption of 44—45 85
Torsion, intrinsic, of a G-structure 44 46—47 87
Torsion, normalization of 46 85 87—88
Total derivative 10
Transformation, classical vii 101 154
Transformation, contact viii 16—17 26—27 56—57 151—155
Transformation, gauge vii 154
Transformation, point viii 26 57 151—155
Translation 27 33 84 115
Wave equation 20
Wave equation, conformally invariant 118—131
Wave equation, homogeneous 39 51
Wave equation, non-linear 79 118—131
Wave operator 118
Wave operator, conformal 120
Weak local minimum 145—149
Weierstrass excess function 148—149
Weierstrass representation 32
Weingarten equation ix 13 26—27 182
Weyl tensor 92 106
|
|
|
| Ðåêëàìà |
|
|
|
|
|
Î ïðîåêòå