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| Guggenheimer H.W. — Differential Geometry |
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| Предметный указатель |
Matrix, Cartan 10
Matrix, continuous 22
Matrix, derivative of 8
Matrix, frame 20 25
Matrix, hermitian 109
Matrix, integral of 10
Matrix, skew-Hermitian 109
Matrix, skew-symmetric 10
Matrix, unitary 109
Maurer — Cartan equations 194
Maximal atlas 203
McCrea, W.H. 260
Mean affine curvature 310
Mean curvature 212 341
Meissner, E. 55
Menger, K. 14
Meusnier, M.C. 216
Midcurve 153
Milnor, J. 197n. 205 255
Minimal surface 219
Minkowski, H. 250 253
Moebius pseudo group 102 147
Moebius strip 205
Moebius, A.F. 101
Mohrmann, H. 155
Montgomery, D. 345 355
Mostow, G.D. 289
Motion 272
Motion, euclidean 21 127 141
Movement, inverse 70
Moving frame 18
Mueller, H.R. 72
Mukopadhaya 30
Multiplication table 92
Multiplication, abelian 86
Natural conditions 179
Natural differentiability condition 144
Natural equation 24
Nevanlinna, F. 245n.
Nevanlinna, R. 245n.
Nijenhuis tensor 361
Nijenhuis, A. 323 354
Nodal Locus 47
Nomizu, K. 348 354 355 364
Normal affinity 95
Normal coordinates 330
Normal curvature 207
Normal indicatrix 161
Normal to surface 207
Normal, affine 151 292 293
Normal, affine, covariant 299
Normal, affine, tangent 309
Normal, length of 12
Normal, polar 12
Normal, tangent 207
Notation, kernel-index 177
Numbers, complex 93
Numbers, dual 163
Object, geometric 2 202
Orientable surface 249
Orientable variety 199
Orthogonal subspace 180
Orthogonality 9
Osculating parabola 151
Ostrowski, A.M. 49 52 72
parabola 13 34 61
Parabola, osculating 151
Parabolic point 213 291
Parabolical convexity 154
Paraboloid, elliptic 301
Paraboloid, hyperbolic 168 302
Parallel set 80
Parallel surface 216
Parallel, Clifford 282
Parallelism, distant 359
Parallelism, Levi-Civita 318
Parameter, affine 336 359
Parameter, differential 329
Parameter, distribution 169
Peano curve 1 3 7
Peano, G. 14
Pfaffian 179
Planar umbilic 213
Plane affine curvature 150 172
Plane vector product 10
Plane, central 221
Plane, focal 259
Pluecker coordinates 163
Podal Curve 13
Poincare Formula 190
Point at infinity 90 225
Point curvature 336
Point, sextactic 152
Poisson bracket 135
Polar coordinates, geodesic 264
Polar normal 12
Polygon, geodesic 283
Pontrjagin, L. 124
Posidonius 282
Prime differentiation 8 15
Principal curvature 210 214 338
Principal curvature radius 253
Principal direction 210
Principal direction of line congruence 257
Principal direction, affine 310
Principal frame 339
Principal surface 257
Principal vector 210
Product, direct 91
Product, Lie 105
Product, scalar 9 262 314—315
Product, vector 10 163
Projection map 201 262
Projection, central 255
Projection, stereographic 225
Projective geometry 146
Projective line 90
Projective space 98
Prolongation 136 140
Property, geodesic 263
Property, geometric 2
Pure deformation 95
Quadric, Lie 312
Quarternion 94 100
Quarternion, unit 101
R 87
Rank 146
Reaumur, R.A.F. de 47
Rectifiable curve 16
Reducible group 347
Reductive algebra 129
Reeb, G. 260
Regression, edge of 167
Reidemeister, K. 313
Representation 87
Representative 2
Revolution, congruence of 259
Revolution, surface of 204 227
Ricci coefficient 317
Ricci identity 324 358
Ricci tensor 325
Ricci — Curbastro, G. 324 341
Riemann curvature 333
Riemann curvature tensor 322
Riemann curvature tensor, recurrent 328
Riemann curvature, scalar 325
Riemann space, irreducible 347
Riemann space, locally euclidean 347
Riemann space, totally reducible 349
Riemann — Stieltjes sum 36
| Riemann, B.F. 16
Riemannian affinity 345
Riemannian homothety 345
Riemannian manifold 314
Riemannian volume 350
Right-hand derivative 17
Rigidity, infinitesimal 246
Rinow, W. 285 286 289
Robinson, G. de B. 346w.
Rodemich, E. 32
Rodrigues, O. 210
Rotation 10 98 128
Rotation, hyperbolic 277
Rothe, H. 102
Roulette 65
Ruling 165
Ruling, umbilical 259
Rund, H. 364
Saban, G. 162 174 216
Samelson, H. 345 355
Sannia, G. 313
Scalar product 9 262 314—315
Scherk, P. 227
Schlafli, L. 335
Schmidt, E. 30 34
Schouten, J.A. 177 354
Schreier, O. 113
Schur differential equation 122
Schur, A. 30
Schur, F. 120 333
Schwarz, H.A. 255
Schwarzian derivative 146
Section 201 262
Section, central 221
Semisimple algebra 114
Sequence, Cauchy 285
Sex tactic point 152
Similitude 58
Similitude, indirect 60
Simple algebra 116
Simple curve 4
Sine theorem, hyperbolic 279
Sine theorem, spherical 267
Sinistrorse curve 170
Skew-Hermitian matrix 109
Skew-symmetric matrix 10
Snell’s law 79
Solid vector product 163
Space curve, tangent surface of 204
Space, complete 285
Space, Einstein 328
Space, flat 359
Space, projective 98
Space, Riemann 347 349
Space, tangent 199
Space, vector 175
Space, Weyl 362
Sphere 198
Sphere, affine 301
Sphere, affine improper 306
Sphere, dual 164
Spherical cosine theorem 271
Spherical curvature 162
Spherical curves 161
Spherical image 212
Spherical sine theorem 267
Spiral of Archimedes 13
Spiral of MacLaurin 13 25 34
Spiral, hyperbolic 13 61
Spiral, logarithmic 7 17 59
Stability group 349
Star-shaped surface 249
Steiner, J. 81 216 227
Stephanos, C. 102
Stereographic projection 225
Stokes formula 192
straight lines 59 143 152
Striction, curve of 166
Strictly convex surface 253
Structure constants 106
Structure,  197
Study, E. 162 164 174
Sturm, J.C.F. 266
Subalgebra 129
Subnormal, polar 12
Subset, invariant 113
Subspace, local 196
Subspace, orthogonal 180
Subspace, totally geodesic 340
Subtangent, polar 12
Summation convention, Einstein 177
Support function 54 55 249
Surface of revolution 204 227
Surface, canal 216 251
Surface, Cayley’s 306
Surface, center 215
Surface, central 259
Surface, closed 197
Surface, complete 285
Surface, convex 249
Surface, isothermal 247
Surface, local 196
Surface, minimal 219
Surface, molding (moulure) 237
Surface, normal to 207
Surface, orientable 249
Surface, parallel 216
Surface, principal 257
Surface, ruled, generator of 165
Surface, star-shaped 249
Surface, strictly convex 253
Surface, tangent, of space curve 204
Surface, translation 305
Surface, Weingarten 237
Surfaces, family of 222
Surfaces, isometric 212
Sydler, J.P. 32
Symbol, Kronecker 104 186
Symmetric tensor 185
Symmetry 26
Tac locus 47
Tachibana, S. 350 363
Tangent cone 169
Tangent image 19
Tangent normal 207
Tangent normal, affine 309
Tangent space 199
Tangent surface of space curve 204
Tangent tensor space 201
Tangent, length of 12
Tangent, polar 12
Tchebychef net 236
Teixeira, G. 13
Tensor connection 363
Tensor field 201
Tensor space, tangent 201
Tensor, coordinate 182
Tensor, Einstein 328
Tensor, Nijenhuis 361
Tensor, Ricci 325
Tensor, Riemann curvature 322 328
Tensor, symmetric 185
Tensor, torsion 358
Tensor, type of 182
Tensor, Weyl 334 337
Theorema egregium 212 234
Thomas, T.Y. 336
Torsion of space curve 157
Torsion, relative 207
Torus 281 287
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