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| Авторизация |
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| Flanders H. — Differential Forms with Applications to the Physical Sciences |
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| Предметный указатель |
Abraham, M. 195 197
Affine connection 143 ff
Affine frame 143
Affine group 164
Alexandroff, P. 197
Ampere's law 45 80
Becker, R. 195 197
Beltrami operator 44
Bi-invariant form 160
Bianchi identity 131
Blaschke, W. 44 197
Boundary of a simplex 58
Bounding cycle (boundary) 63
Bourbaki, N. 197
Brackets 179 ff
Buck, R.C. 197
Caratheodory, C. 104 197
Cartan, E. 3 4 96 99 108 176 197
Cauchy problem 4
Chains 61 ff
Chern, S.S. 198
Chevalley, C. 197
Christoffel symbols 129
Closed form 67
Commutative diagram 56
Completely integrable system 96
Complex projective space 73
Compound (of a transformation, matrix) 11 ff
Connection coefficients 129 144
Constants of structure 151
Contact transformation 183 ff 185
Continuity equation (fluids) 189
Convex surface 112
Curvature forms 122 144 148
Curvature matrix 122 130
CYCLE 63
Cylinder construction 27 ff
De Rham's theorems 66 ff
de Rham, G. 197
de Saint-Venant, B. 195
Debever, R. 198
Degree of a mapping 77 ff
Dirichlet integral 83
electromagnetic field 16 44
Euler equation of motion 191
Exact form 67
Exterior derivative 20 ff
Exterior multiplication 8 ff
Faraday's law 45
First integral 107 182
Flanders, H. 198
Flat Riemannian manifold 135
Fluid mechanics 188 ff
Flux 43
Frame manifold 146
Frenet formulas 122
Frobenius integration theorem 92 ff
Frobenius, G. 4
Gallissot, F. 198
Gauss integral 79
Gauss mean value theorem 85
Gauss, C.F. 43
Gaussian curvature 42 118 126
General linear group 156
Geodesic 119 134
Goldberg, S.I. 198
Golomb, M. 198
Goursat, E. 4 26 198
Grammian (Gram determinant) 12
Green's formulas 83
Green's function 86
Hadamard, J. 198
Hamilton — Jacobi equation 186
Hamiltonian 166
Hamiltonian equations of motion 167
Hamiltonian systems 166 ff
Heat equation 90 ff
Helmholtz law of conservation of vorticity 193
Hodge, W.V.D. 15 136 138 198
Homogeneous contact transformation 183
Hopf invariant 79
Hopf, H. 197
Hypersurfaces 116 ff
Infinitesimal contact transformation 187
Infinitesimal transformation 37
Injection (imbedding) 63
Integral surfaces 92
Integral-invariant 174
Jacobi identity (relation) 180 181
Jordan — Brouwer theorem 77
Kaehler, E. 4
Kinetic potential 166
| Klein bottle 71
Kronecker integral 77
Lagrange brackets 183
Lagrangian 166
Lamb, H. 198
Laplace expansion (determinant) 10
Laplacian 38 ff 44 82
Last multiplier 107
Left invariant, form 150
Left translation 160
Lie bracket 180
Lie group 150 ff
Lie, S., third theorem of 108
Line of curvature 120
Linking number 79 ff
Liouville theorem (harmonic functions) 88
Liouville theorem (phase space) 178
Local coordinate neighborhood 49 ff
Lorentz inner product (or metric) 12 46
Love, A.E.H. 195 198
Manifold 49 ff
Maximum principle 85
Maxwell's equations 16 44
Mayer, A., system of 104
Mean curvature 42 118 126
Minimal surface 44
Misner, C.W. 198
Momentum components 166
Monge notation 126
Moving frames 4 32
Nickerson, H.K. 198
Ordinary differential equations 106 ff
Orientable manifold 51
Orientation (linear space) 15
Orthogonal coordinates 39
Orthogonal group 158
Orthonormal basis 13 ff
p-vector 5 ff
Parabolic equation 90
Parallel displacement 119 133 145
Parallel surface 113
periods 66 ff
Phase density 10 164
Phase space 163
Poincare lemma 2 4 27
Poincare metric (half-plane) 134
Poincare, H. 4
Poisson brackets 180
Poisson integral formula 87
Position space 163
Potential theory 82 ff
Poynting vector 47
Principal curvatures 42 120
Principal directions (hypersurfaces) 120
Projective plane 70
Projective space 73
Proper affine group 154
Proper orthogonal group 158
Relative integral-invariant 176
Riemann curvature tensor 122 131
Riemannian geometry 4 127
Right invariant form 151 159
Right translation 151
Seifert, H. 77 198
Signature (inner product) 13
Simplex, simplices 57 ff
Sommerfeld, A.J.W. 198
Special linear group 157
Spencer, D.C. 198
Spherical coordinates 34
Spherical harmonics 142
Standard n-simplex 60
Star operator 15 ff
State space 165
Steenrod, N. 198
Step transformation group 155
Stokes' theorem 2 64
Submanifold 52
Support function 114
Surfaces, differential geometry of 40 ff 112
Tangent vectors 53 ff
Tensors 2 ff
Threlfall, W. 77 198
Torsion 144 148
Trajectory 171
Umbilic point 148
Unimodular group 157
Vector field 54 179
Vorticity 192
Wheeler, J.A. 198
Whittaker, E.T. 198
Willmore, T.J. 198
Winding number 77 ff
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