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Eisenhart L.P. — Transformations of surfaces
Eisenhart L.P. — Transformations of surfaces

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Название: Transformations of surfaces

Автор: Eisenhart L.P.

Язык: en

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1923

Количество страниц: 379

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint equation      9 22 88 93
Angle, of two hyperplanes      2
Angle, of two lines      1
Angle, of two spheres      234
Angle, of two surfaces in pentaspherical coordinates      282
Applicable nets, and congruences of circles      272
Applicable nets, and cyclic systems      274
Applicable nets, definition      61
Applicable nets, parallel to given pair      62
Applicable nets, transformations F of      61 275 290 325 334
Applicable nets, which are 2, O      298. See Nets C and Nets permanent in deformation.
Applicable nets, which are O      286
Asymptotic lines, definition      98
Asymptotic lines, determination of      356
Asymptotic lines, in Lie line-sphere transformation      252
Asymptotic lines, parametric      99 123
Axis congruence, definition      125
Axis curves, definition      125
Axis curves, form a net      125 153
Axis curves, property of      126
Beltrami      272 299 310 312 314
Bianchi      112 138 142 143 180 209 210 212 214 215 216 229 230 292 298 301 305 308 310 312 316 317 320 327 344 345 352 356 360 362 363 366 371 372
Bonnet      295 317
Calapso      225 230 232 286 298 319 320 331
Calo      318
Chieffi      316
Christoffel transformations and transformations $D_m$      229
Christoffel transformations of isothermic surfaces      229 286
Christoffel transformations of special isothermic nets      230 291
Christoffel transformations, nets determined by      319
Circle-planes of a transformation R, coincident for two transformations      206 211
Circle-planes of a transformation R, definition      198
Circle-planes of a transformation R, envelope of      199 213 285 286
Circle-planes of a transformation R, pass through a point      200 230
Circles K, definition      202
Circles K, form a congruence      263
Circles K, normals to nets at points of      204
Circles K, of the first kind      206
Circles K, of the second kind      206 229
Congruence K, cyclic      206
Congruence K, definition      203
Congruence K, focal points of      229
Congruence of rolling      316
Congruence of rolling, developables of      317
Congruence of rolling, focal surfaces of      317
Congruence of rolling, normal      321
Congruence of rolling, parallel      321
Congruence of rolling, pseudospherical      321
Congruence of rolling, with coincident developables      317
Congruence of rolling, with constant focal segment      321
Congruence R, definition      113
Congruence R, focal surfaces      115
Congruence, conjugate to a net      12 15 34
Congruence, conjugate to O nets      167
Congruence, conjugate, of a transformation F      34
Congruence, definition      11
Congruence, developables of      11
Congruence, direction equation of      13 153
Congruence, focal points of      11
Congruence, focal surfaces of      11
Congruence, harmonic to a net      22 24 25 29 80 81 153
Congruence, harmonic to a point net      28
Congruence, harmonic, of a transformation F      40 153
Congruence, middle surface      16 21 32
Congruence, normal to a net      168
Congruence, parallel      15
Congruences 2, I, normal      159 294
Congruences I and p, I, definition      158
Congruences of circles, a cyclic system      272 274 278 285
Congruences of circles, characteristic property      243
Congruences of circles, definition      241
Congruences of circles, envelope of planes of      258 259 269 270 271 274
Congruences of circles, focal points of      243
Congruences of circles, focal spheres of      241
Congruences of circles, in cartesian coordinates      243
Congruences of circles, parallel transformations of      272
Congruences of circles, transformations F of      269 270
Congruences of spheres and circles, conjugate      261—263 270
Congruences of spheres and circles, harmonic      255—259 264 265 267 269—271
Congruences of spheres and circles, orthogonal      266 267 285
Congruences of spheres, chords of contact of      239
Congruences of spheres, cutting a fixed sphere under constant angle      283
Congruences of spheres, definition      238
Congruences of spheres, derived      240 243
Congruences of spheres, focal circles of      239 241
Congruences of spheres, in cartesian coordinates      243
Congruences of spheres, null-spheres      243 284
Congruences of spheres, principal curves of      238
Congruences of spheres, with applicable central nets      271
Congruences R of spheres, definition      246
Congruences R of spheres, direction-equation with equal invariants      255
Congruences R of spheres, parallel      246
Congruences R of spheres, permanent in deformation      298 308 310
Congruences R of spheres, representation in 5-space      285
Congruences R of spheres, transformations F of      246
Congruences, nets conjugate to      159 168
Conies, pencil of      95
Coordinates, Cartesian      1
Coordinates, homogeneous point      69
Coordinates, of a sphere      233
Coordinates, pentaspherical      see Pentaspherical
Coordinates, tangential      97 166 286
Cosserat      206
Curve, definition      2 71
Curve, parametric      2
Cyclic congruences, characteristic property      280 285
Cyclic congruences, definition      183
Cyclic congruences, generation of      289
Cyclic congruences, multiply      185 188 191
Cyclic congruences, parallel      191
Cyclic systems, circles pass through a point      191
Cyclic systems, definition      183
Cyclic systems, envelope of planes of      199 213 285 286
Cyclic systems, generation of      272—274 285 289
Cyclic systems, of a transformation R      197 206 285
Cyclic systems, representation in 5-space      277—279
Cyclic systems, transformations F of      275 277 278 290
Cyclides      283
Darboux      6 92 147 154 208 212 213 239 254 274 281 282 283 285 288 291 295 313 317 358
Deform of a quadric, which meets the circle at infinity in 4 points      291
Deform of revolution      293—296 305 360
Deform permanent nets on      326—329 353
Deform R nets on      327 328
Deform tangent to the circle at infinity      317
Deform transformations $B_k$ of      340—352 354—356
Deform transformations $F_k$ of      334—340 346 353 354
Deform transformations H of      366 371 372
Demoulin      107 108 112 113 115 119 124 134 150 202 204 220 225 229 254 284
Derivant net, definition      25
Derivant net, of two transformations F      54
Derivant net, of two transformations K      61
Derivant net, of two transformations R      265
Derived congruences, definition      21
Derived congruences, of a W congruence      108
Derived congruences, of spheres      240 241
Derived net, definition      25
Derived net, Laplace transforms of a      32 33
Derived net, of two transformations F      54
Derived net, parallel      33 53
Derived net, reciprocally      116
Derived net, transformations F of      54 66
Derived net, which is O      289
Developable surface, definition      10
Developable surface, of a congruence      11
Dini      362
Direction-parameters, of a congruence      12 14 20 30
Direction-parameters, of a cyclic congruence      183 281
Direction-parameters, of a line      1
Drach      155
Envelope of rolling, definition      305
Envelope of rolling, lines of curvature      320
Envelopes of spheres, conformal mapping of the two sheets      206 286
Envelopes of spheres, congruence of chords of contact      239 241 242 244 245 258 259 285
Envelopes of spheres, cutting a fixed sphere under constant angle      283
Envelopes of spheres, principal curves on      238 239 243
Envelopes of spheres, with applicable central nets      272 274 298 302 307 308 310
Envelopes of spheres, with O nets corresponding      174 189 229
Envelopes of spheres, with spherical lines of curvature      285
Equation, direction, of a congruence      13 153
Equation, point, of a net      3 72
Equation, tangential, of a net      128 153
Focal circles of a congruence of spheres      239 241
Focal nets in relation F      34
Focal nets of a congruence      11 15
Focal nets of parallel congruences      21
Focal nets radial transforms      33
Focal nets, coordinates of      10 14 29
Focal nets, of a congruence of circles      245
Focal nets, of a ray congruence      124
Focal points, of first and second rank      11
Focal spheres of a congruence of circles      241
Focal spheres, meeting orthogonally      183
Focal surfaces of a congruence      11 15
Green      124 125 126
Guichard      5 12 26 - 156 165 200 255 258 262 263 266 280 285 295 296 337
Hammond      77 85 87 93 94
Homogeneous point coordinates      69
Homogeneous point coordinates, of a net in 2-space      96
Homogeneous point coordinates, of a net in 3-space      101 103
Homogeneous point coordinates, of an R net      107
Hyperplane at infinity      69
Hyperplane, definition      2
Hyperquadric, net on      90 254
Hyperquadric, transformations F of nets on      90 94
Hyperspheres, focal      183 185
Hyperspheres, in transformations R      171 174 189
Invariants equal to zero      73 92
Invariants in a sequence of Laplace      75 92
Invariants of an equation of Laplace, definition      16
Inversion, in pentaspherical coordinates      281
Inversion, in transformations M      175
Inversion, of a cyclide      283
Inversion, of a sphere      281
Isothermal-conjugate nets, and nets with equal point invariants      125 150
Isothermal-conjugate nets, characteristic property      126
Isothermal-conjugate nets, definition      104
Isothermal-conjugate nets, on a deform of a quadric      326
Isothermal-conjugate nets, on a quadric      112 367 372
Isothermal-conjugate nets, preserved by projective transformation      104
Isothermal-conjugate nets, R nets are      107
Isothermic O nets, are nets $\Omega$      231
Isothermic O nets, definition      206
Isothermic O nets, in pentaspherical coordinates      237
Isothermic O nets, Lie transformation of      284
Isothermic O nets, nets with the same spherical representation as      302—304 318 319
Isothermic O nets, special      212—214 291
Isothermic O nets, spherical representation of      319. See Transformations $D_m$ and Chiristoffel transformations
Isotropic, line      289 291 296
Isotropic, plane      289 296
Isotropic, relation      157
Jonas      42 47 110 113 119 201
Kinematically conjugate directions, auto-conjugate      815 320
Kinematically conjugate directions, axes of rotation      315
Kinematically conjugate directions, definition      314
Kinematically conjugate directions, for congruences of rolling      317 321
Kinematically conjugate directions, orthogonal      320
Kinematically conjugate directions, parametric      320
Koenigs      58 123
Laplace equations      3 12
Laplace equations, invariants of      16
Laplace equations, Moutard form      237
Laplace equations, sequence of      74
Laplace transforms, definition      17
Laplace transforms, in cartesian coordinates      17
Laplace transforms, in homogeneous coordinates      72
Laplace transforms, in tangential coordinates      129
Laplace transforms, of a derived net      32 33
Laplace transforms, of a function      19 32
Laplace transforms, of a net R      108
Laplace transforms, of a radial transform      33
Laplace transforms, of parallel nets      18
Laplace transforms, transformations F of      66 94
Laplace transforms, which are O nets      192 193 286
Levy sequences, of higher order      83—85 93
Levy sequences, of the first order      81 93
Levy sequences, periodic      85 86
Levy transforms, and transformations F      66
Levy transforms, definition      19
Levy transforms, in a hyperplane      81
Levy transforms, in homogeneous coordinates      81
Levy transforms, of parallel nets      32
Levy transforms, of radial transforms      33
Lie      249 283 284
Lie line-sphere transformation, equations of      249 283
Lie line-sphere transformation, linear complex of      249 284
Lie transformations of surfaces, definition      252
Lie transformations of surfaces, equations of      283 284
Lie transformations of surfaces, W congruence of      253
Linear complex, definition      248
Linear complex, lines conjugate with respect to      250 251 284
Linear complex, null-plane of      248 251 252
Linear complex, special      248
Linear complex, tangents to a curve lines of a      284
Martin      32
Minimal surfaces, deformable transformations R of      304 305
Minimal surfaces, focal sheets of a W congruence      230
Minimal surfaces, in relation R      296 308
Minimal surfaces, O net of      229
Minimal surfaces, transformations $D_m$ of      215 217
Nets $\Omega$, and nets R      254
Nets $\Omega$, definition      218
Nets $\Omega$, equations of      219 220
Nets $\Omega$, isothermic      231
Nets $\Omega$, on surfaces of Guichard      225 232
Nets $\Omega$, parallel      221
Nets $\Omega$, transformations R of      221—224
Nets $\Omega$, with isothermal spherical representation      231
Nets 2, O, applicable      298
Nets 2, O, as central nets of transformations R      171 189
Nets 2, O, associated with cyclic systems      279
Nets 2, O, definition      156
Nets 2, O, on quadrics of revolution      247
Nets 2, O, special      188 228
Nets 2, O, transformations F of      189—191
Nets C, congruences harmonic to      287 288.
Nets C, definition      200
Nets C, harmonic to a normal congruence      200
Nets C, on the envelope of planes of a cyclic system      200
Nets corresponding with orthogonality of linear elements      63 146
Nets corresponding with orthogonality of linear elements, parallel      64
Nets corresponding with orthogonality of linear elements, transformations F of      64—66
Nets G, definition      192
Nets G, Laplace transforms of      192 286
Nets G, parallel      192
Nets G, radial transforms of      193
Nets G, transformations F of      193
Nets O, congruences conjugate to      168
Nets O, conjugate to congruences I      2 1 1 160
Nets O, definition      156 194
Nets O, derived      289. See Isothermic O nets
Nets O, determination of      165—167
Nets O, generated by a rolling surface      289 291 294
Nets O, in 5-space and cyclic systems      277
Nets O, in pentaspherical coordinates      237 279
Nets O, inversion of      175
Nets O, on a hypercone      191 283
Nets O, on a hypersphere      167
Nets O, parallel      167
Nets O, radial transformations of      175
Nets O, transformations F of      168—175 185—188
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