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| Авторизация |
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| Montiel S., Ros A. — Curves and Surfaces |
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| Предметный указатель |
Alexandrov 172 187
Ampere 2
Arc length 1
Archimedes 161
Area 141
Bartels 2
Bernouilli, D. 1
Bernouilli, John 1 206
Bernouilli, Joseph 2
Bertrand 68
Bianchi 31
Binormal 2 14
Binormal line 22
Blaschke 172
Bonnet 182 204 276 296 302
Brower 108 116 118 161 288 310
Brunn 173 189 311 325
Brunn — Minkowski inequality 189 325
Catenoid 95 239
Cauchy 2 32 205
Chain rule 48
Chasles 68
Chern 156
Circumscribed circle 346
Clairaut 2 31 240
Cohn — Vossen 205 218
Comparison of curves 22
Comparison of lines and surfaces 111 112
Comparison of planes and surfaces 113
Comparison of surfaces 96
Cone 38 39
Congruence 207
Connected component 36
Crofton 312 343
Curvature, centre 21
Curvature, Gauss 68 77
Curvature, mean 68 77
Curvature, of a curve 1
Curvature, of a curve, in  14
Curvature, of a curve, plane 10
Curvature, radius 1
Curvature, total 330
Curve 3
Curve, convex 328
Curve, coordinate 35
Curve, integral 258
Curve, knotted 345
Curve, on a surface 42
Curve, p.b.a.l. 9
Curve, parallel 321
Curve, parametrized 313
Curve, periodic 314
Curve, regular 8
Curve, simple 38 313 318
Cylinder 37 44 71 80 95 225
Darboux 2 68 240
Darboux, trihedron 240
Degree between curves 365
Degree between surfaces 277
Degree, local 281
Dependence of parameters 149
Descartes folium 314
Diffeomorphism 43
Diffeomorphism, local 54
Differential 46 48
Diquet 241
Distance 239
Divergence 157 322
Divergence, on surfaces 184
Domain, inner 118 174
Domain, inner of a curve 320
Domain, outer 118
Domain, outer of a curve 320
Domain, regular 159
Dominated convergence 148
Dupin 2
Efimov 173
Ellipsoid 36 37 80 174
Equations, Darboux 240
Equations, Frenet 10
Euler 1 31 67 206 312
Euler, characteristic 295 302 304
Evolute 21
Evolvent 21
Existence and uniqueness, theorem of 17 227
Exponential map 230
Fary 312 345
Fenchel 312 342
Field, conformal on a sphere 292
Field, conservative 351
Field, non-degenerate 289 292
Field, normal 69 119
Field, on  322
Field, on 157
Field, on a surface 69
Field, tangent 69 257
First fundamental form 68 207
First integral 259
Flow of a field 258
Formula, area 152
Formula, Bertrand — Puiseux 241
Formula, change of variables 144
Formula, Crofton 343
Formula, Diquet 241
Formula, Gauss — Bonnet 296 302
Formula, Herglotz 217
Formula, integration in polar coordinates 147
Formula, length 321
Formula, Poincare — Hopf 302
Formula, variation of area 193
Formula, variation of length 222
Formula, variation of volume 194
Formulas, Frenet 16
Formulas, Green 351
Formulas, Minkowski 184
Four-petal rose 313
FOURIER 2
frenet 2 16
Frenet, dihedron 9
Frenet, trihedron 14
Fubini 146
Function, differentiable 40
Function, distance 41 87
Function, height 41 85 87 301
Function, implicit 36 49
Function, integrable 139
Function, inverse 58
Function, on a sphere 150
Function, support 94 177
Gauss 2 31 68 157 172 203 210 232 275 296 302
Gauss, Lemma 232
Gauss, map 68 76
Geodesic 1 223
Geodesic, ball 232
Geodesic, existence 228
Geodesic, homogeneity 229
Geodesic, minimizes locally 233
Germain 68
Gluck 313
Gradient 161
Gradient, on surfaces 197
Graph 35 53 71
Grauenstein 312 331
Green 157
Gromov 311
Group of isometries 209
hadamard 172 175 178 311
Hartman 173 273
Heintze 173 186
Heintze — Karcher’s inequality 186
| Helein 311
Helicoid 91 239
Helix 4 16 19 22
Herglotz 205 217 312
hessian 85 87
hilbert 91 172
Hopf 206 238 312
Hurwitz 311
Hyperboloid 37 44
Index of a field 289
Index, rotation 329
Integral on  137
Integral on a surface 139
Isometry 208
Isometry, local 207
Isoperimetric inequality in the plane 326
Isoperimetric inequality in the space 195
Jackson 312
jacobi 206
Jacobian 76 277
Jacobian, absolute value 57 136
Jacobian, on curves 368
Jellett 91 172 185
JORDAN 107 116 310 320
Karcher 173 186
Kelvin 135
Kneser 312
Kramer 31
Lagrange 205
Lancret 2 23
Laplace 2
Laplacian 351
Laplacian on 164
Laplacian on surfaces 197
Lashoff 156
legendre 275
Leibniz 1
Length of a curve 7
Length of a periodic curve 315
Length, arc 5 8
Liebmann 91 172 184 205
Liouville 206
Logarithmic spiral 9
Malus 2
Map, constant 41
Map, differentiable 40
Map, identity 41
Map, inclusion 41
Massey 173 273
Maxwell 135 311
Measure zero 126 131
Measure zero on a surface 142
Meusnier 2 68
Milnor 312 345
Minding 172 205 241
Minkowski 172 189 311 325
Moebius strip 71 74
Monge 1 31 67
monodromy 196
Monotone convergence 148
Mukhopadhyaya 312
Myers 182
Neighbourhood, coordinate 35
Neighbourhood, normal 236
Neighbourhood, tubular 122
Neighbourhood, tubular, of a curve 321
Newton 1
Nirenberg 173 273
Normal, line 8 319
Normal, of a curve, in the plane 9
Normal, of a curve, in the space 14
Normal, of a surface 46 51
Normal, sections 81
Oresme 1
Orientation 119
Orientation, of curves 319 320
Orientation, of surfaces 70
Orientation, preserving 76
Oriented distance 125
Osculating, circle 21
Osculating, plane 23
Osserman 313 346
Oval 328 329
Ovaloid 172 174
Ovaloid, intersection with lines 177
Pappus 311
Paraboloid 37 90 174 256
Paraboloid, hyperbolic 80
Parametrization 35
Parametrization, by curvature lines 261
Parametrization, change of 39 40
Parametrization, orthogonal 95 261
Partition of unity 143
Period of a periodic curve 314
Poincare 276 295 302
Point, critical 48
Point, elliptic 83 87
Point, hyperbolic 83 87
Point, of double intersection 115
Point, of first contact 115
Point, parabolic 83
Point, planar 83
Point, umbilical 83
poisson 2
Poncelet 2
Principal curvatures 78
Principal directions 79 84
Projection 125
Ptolemy 31
Puiseux 241
Quadric 37 80
Region of a surface 136
Regular value 36 111
Reilly 173
Reparametrization 8
Reparametrization by arc length 9
Riemann 32 239
Rigid motion 7 80 144 207
Rinow 206 238
Rodrigues 2 68
Rustihauser 312
Saint-Simon 68
Saint-Venant 2
Samelson 108 118 312
Sard 112 132 311 321
Schmidt 311
Schwarz 173
Second fundamental form 68 76 77 207
Second variation of the length 253
Segre 312
Senff 2
Separation, global 116
Separation, local 108
Serret 2
Sphere 36 45 71 79 143 145 213 292
Steiner 173
Stoker 172 175 178 273 311
Stokes 135 157 311
surface 32 34
Surface, convex 174
Surface, of revolution 55 163
Surface, orientable 70
Surface, oriented 70
Surface, parallel 123 145 147
Surface, star-shaped 57 95 177
Surface, strictly convex 175
Surface, triply periodic 56
Surface, umbilical 84
Surface, with parallel s.f.f. 263
Surfaces, congruent 207
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