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Bryant R., Griffiths P., Grossman D. Ч Exterior differential systems and Euler-Lagrange PDEs
Bryant R., Griffiths P., Grossman D. Ч Exterior differential systems and Euler-Lagrange PDEs



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Ќазвание: Exterior differential systems and Euler-Lagrange PDEs

јвторы: Bryant R., Griffiths P., Grossman D.

язык: en

–убрика: ћатематика/јнализ/ƒифференциальные уравнени€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2002

 оличество страниц: 205

ƒобавлена в каталог: 06.04.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Admissible lifting      156Ч161 165
Affine frame bundle      58Ч65
Affine fundamental forms      59Ч65 73
Affine hypersurface      37 57Ч65 73 74
Affine normal line      60Ч63
Affine transformation      x 58Ч65
Area functional      vii 15 24Ч35
Asymptotic curve      184 190
Backlund transformation      xi 23 188 190Ч197
Basic form      xii 57
Betounes form      xi 158Ч164
Bianchi identity      91Ч92
Bianchi, L.      193
Blaschke, W.      61
Calibration      145Ч149 156
Cartan lemma      24 59 60 94 108
Cartan, E.      ix xi 37
Cauchy problem      118Ч120
Cauchy Ч Schwarz inequality      129
Characteristic cohomology      4
Characteristic system      183Ч185
Christodoulou, D.      118
Coframe bundle      38
Conformal bundle      104
Conformal curvature      82
Conformal energy      127
Conformal flat model      79Ч85 91 96Ч100 102 115Ч118
Conformal frame bundle      83 85
Conformal group      40 79 97 101 111 139
Conformal inner-product      80 83 136
Conformal Laplacian      79 80 93Ч97 102 120 138
Conformal structure      x 79Ч110 133 136Ч140 149
Connection      42 52
Connection, Cartan      85 91 137
Connection, Levi Ч Civita      22 77 87 95 141 142
Conservation law      ix 14Ч21 79
Conservation law for $\square z = Cz^{\frac{n+3}{n-1}}$      123Ч127
Conservation law for $\triangle u = Cu^{\frac{n+2}{n-2}}$      110Ч118
Conservation law for cmc hypersurfaces      32Ч34
Conservation law for harmonic maps      166Ч168
Conservation law for K = -1 surfaces      183Ч190
Conservation law for minimal hypersurfaces      27Ч32
Conservation law for wave equations      118Ч127
Conservation law, higher-order      176Ч190
Conservation law, proper      15 18Ч19
Conservation law, trivial      15 116 188
Conservation law, УalmostФ      34Ч35 125
Conservation law, УhiddenФ      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 1Ч8 10 39 77 83 97
Cotten tensor      92
Covariant derivative      90 92 94 95 109 138Ч144 165
Darboux theorem      50
Decomposable form      41 53 183
Density line bundle      92Ч97 124 126 138 149
Dilation      34 84 116 121 123
Divergence equivalence      155 156
Energy      vii 122Ч123 127Ч129
Energy of a map      164 165
Equivalence method      ix 37Ч38 41Ч53 65Ч74 79 85Ч88 102Ч110 134
Equivalence of conformal structures      85Ч92
Equivalence of G-structures      42
Equivalence of Lagrangians      3
Equivalence of Monge Ч Ampere systems      39Ч 52
Equivalence of Poincare Ч Cartan forms      65Ч78 102Ч110
Euclidean frame bundle      21 26 28 182
Euclidean motion      21Ч34 78
Euclidean space      vii 21Ч35
Euler Ч Lagrange equation      vii viii 7 10 72 99 151 156
Euler Ч Lagrange system      ix 1 7Ч15 40 51 133Ч149
Exterior differential system      xii
Field      147Ч150
First variation      viii 7 133Ч134
Frobenius theorem      55
Functional      viiЧix 3Ч7
G-structure      37Ч38 41Ч50 85Ч88 102
Gauss curvature      13 41 182Ч197
Gauss map      23
Generating function      16Ч17
Grassi, M.      155n 163n
Grassmannian      2 13 56 142 151
GreenТs Theorem      viii 127Ч130
Harmonic function      29
Harmonic map      xi 164Ч168
Hodge Ч Lepage decomposition      4
HolderТs Inequality      130
Holomorphic curve      31Ч32
Ideal, algebraic      2n 154
Ideal, differential      2 9 10 158
Independence condition      2 20
Integrable extension      xi 185Ч188
Integral manifold      xii 2 4 15
Integral manifold, transverse      12
Inverse problem      1 7 10Ч14 24 39 51
inversion      84 117 121 125
Jacobi operator      ix 145 149Ч150
Jets      vii 2 99Ч100 103
John, F.      129
K3 surface      13
Killing vector fields      166
Koszul complex      144
Lagrangian      viiЧix 3Ч7 155Ч164
Lagrangian potential      57Ч58 73 145
Laplace equation      139
Legendre submanifold      2Ч3 7Ч11 133Ч145 158
Legendre submanifold, non-transverse      23 27 196
Legendre submanifold, transverse      3 9 142
Legendre variation      7Ч9 134Ч149
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 Ч Cartan equation      58 82
Maurer Ч Cartan form      80Ч82 85 100 167
Mean curvature      vii 13 24
Mean curvature, constant      24 27 141
Mean curvature, prescribed      x xi 38 74 77 105n 133 140Ч145
Minimal surface      ix 15 24Ч35 78 145
Minkowski space      20 118Ч127
Minkowski space, compactified      119
Moment conditions      31Ч34
Monge Ч Ampere system      10Ч14 99
Monge Ч Ampere system, hyperbolic      ix 40Ч52 182
Moving frames      59
Multi-contact geometry      151Ч158
NoetherТs theorem      ix 1 7 10 14Ч21 28 29 79 114 115 163 184
Non-degenerate, 1-form      1
Non-degenerate, affine hypersurface      59Ч60
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?zaevТs theorem      117
Poincar?e lemma      11 50 55
Poincare Ч Cartan form      ix 1 6Ч11 133Ч147 151Ч164
Poincare Ч Cartan form, almost-classical      52Ч56 65Ч67
Poincare Ч Cartan form, conformally invariant      97Ч118
Poincare Ч Cartan form, definite      67Ч74 102Ч110 135
Poincare Ч Cartan form, Euclidean-invariant      25Ч26
Poincare Ч Cartan form, neo-classical      x 37 52Ч59 65Ч67 74Ч78 98
Poisson equation      x 11Ч13 79
Poisson equation, conformally invariant      110Ч118
Poisson equation, non-linear      96Ч97 102Ч110 118 188
primitive      4 9n 10Ч12 39Ч40
Principal direction      183
Prolongation of a G-structure      x 42 85Ч88
Prolongation of a linear Lie algebra      87
Prolongation of an EDS      183
Pseudo-connection      42Ч52 85Ч90 103
Pseudosphere      23
Pseudospherical line congruence      192Ч195
Ricci curvature      95
Riemann curvature tensor      22 78 89 105 137 142
Riemannian frame bundle      22 77 95 141Ч144 164
Riemannian Laplacian      96 144
Riemannian manifold      22 74 87
Riemannian metric      77Ч78 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 133Ч140
Second variation for prescribed mean curvature      140Ч145
Semibasic form      xii 38 43 57
Simple foliation      56 78n 97 104
Sine-Gordon equation      xi 185Ч188 190Ч195
Space-like hypersurface      78
Spencer cohomology      44 87
Stationary      viiЧix 7Ч10 134Ч149
Stereographic projection      79 119
StokesТ Theorem      147Ч148
Strauss, W.      121n
Stress-energy tensor      166
Strong local minimum      145Ч149
Summation convention      68
Symbol      10 162
Symmetric form      159 165
Symmetry      ix 14Ч21 78Ч85 102 111Ч113 136
Symmetry, generalized      188
Symmetry, hidden      188
Symplectic linear algebra      4Ч6 10 11 17Ч18 50 164
Symplectic transformation      39Ч40
Tautological 1-form      38 42Ч50 85
Time-orientation      80
Torsion of a pseudo-connection      43Ч52 85Ч90 103
Torsion, absorption of      44Ч45 85
Torsion, intrinsic, of a G-structure      44 46Ч47 87
Torsion, normalization of      46 85 87Ч88
Total derivative      10
Transformation, classical      vii 101 154
Transformation, contact      viii 16Ч17 26Ч27 56Ч57 151Ч155
Transformation, gauge      vii 154
Transformation, point      viii 26 57 151Ч155
Translation      27 33 84 115
Wave equation      20
Wave equation, conformally invariant      118Ч131
Wave equation, homogeneous      39 51
Wave equation, non-linear      79 118Ч131
Wave operator      118
Wave operator, conformal      120
Weak local minimum      145Ч149
Weierstrass excess function      148Ч149
Weierstrass representation      32
Weingarten equation      ix 13 26Ч27 182
Weyl tensor      92 106
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