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Название: Transformations of surfaces

Автор: Eisenhart L.P.

Язык: Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1923

Количество страниц: 379

Добавлена в каталог: 16.04.2005

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 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 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 of      340—352 354—356 Deform transformations 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 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 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 of      215 217 Nets , and nets R      254 Nets , definition      218 Nets , equations of      219 220 Nets , isothermic      231 Nets , on surfaces of Guichard      225 232 Nets , parallel      221 Nets , transformations R of      221—224 Nets , 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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