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| Guggenheimer H.W. — Differential Geometry |
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| Предметный указатель |
Efimov, N.W. 260
Ehresmann, C. 125 154 155 205 363
Einstein space 328
Einstein summation convention 177
Einstein tensor 328
Eisenhart, L.P. 154 174 259 347 354
Element of arc length 202
Element, curvature 50 52
ellipse 17 32 33 45 53 54 61 97 101
Ellipsoid 102 220 228 268 271
Elliptic affine curvature 292
Elliptic geometry 274
Elliptic paraboloid 301
Elliptic point 212 291
Enforced curvature 339
Engel, F. 154
Enneper, A. 217
Envelope 43
Epicycloid 61
Epitrochoid 71
Equidistant curves 278
Erdmann’s condition 79
Erlangen program 139
Euclidean curve 28
Euclidean geometry 274
Euclidean motion 21 127 141
Euler angles 99
Euler characteristic 284
Euler formula 211
Euler, L. 59 67 72 76 77 85 94 101 211 289
Evolute of conic 70
Evolute, affine 153
Evolute, nth 60
Evolutoid 46
Extensor 361
Exterior differential 189
Fabricius-Bjerre, F. 54 154 155
Families of surfaces 222
Families, conjugate 216
Families, triply orthogonal 223
Favard, J. 155 174 205 354
Fenchel, W. 85 252 253
Fermat’s principle 78
Fermi, E. 335
Field 264
First integral 137
Flat space 359
Focal plane 259
Fog, D. 32 34
FORM see “Fundamental form”
Form, differential 179
Form, vector-valued 199
Four-vertices theorem 30 39
Frame 8 18
Frame matrix 20 25
Frame, admissible 356
Frame, Darboux 210
Frame, Darboux, affine 293
Frame, e 315 356
Frame, Frenet 150
Frame, i 315 357
Frame, moving 18
Frame, principal 339
Frenet equation 20 157
Frenet frame 150
Frenet, F. 26
Freudenthal, II. 102 120 124
Friction, dry 56
Frobenius — Cartan theorem 243
Fundamental form, first 202
Fundamental form, first, affine 297
Fundamental form, first, of line congruence 257
Fundamental form, second 209
Fundamental form, second, affine 298
Fundamental form, second, of hypersurface 338
Fundamental form, second, of line congruence 257
Fundamental form, third 216
Gauss affine curvature 310
Gauss curvature 212
Gauss curvature, induced 342
Gauss — Codazzi — Mainardi equations 209
Gauss, C.F. 240 283 289
Gears, dented 62 71
General affine invariant 153
Generalized Kronecker symbol 186
Generator of ruled surface 165
Genus 284
Geodesic 240 263
Geodesic biangle 286
Geodesic circle 271
Geodesic curvature 207
Geodesic curvature, first 339
Geodesic polar coordinates 264
Geodesic polygon 283
Geodesic property 263
Geodesic, affine 309 311
Geographic map 247
Geometric invariant 138
Geometric object 2 202
Geometric property 2
Geometry, elliptic 274
Geometry, Euclidean 274
Geometry, hyperbolic 275
Geometry, k-point 138
Geometry, Klein 139
Geometry, locally euclidean 275
Geometry, projective 146
Golab, S. 154
Grassmann algebra 188
Graves, L.M. 34n.
Green’s formula 350
Group 86 (see also “Holonomy group”)
Group, reducible 347
Group, stability 349
Groupoid 90
Hadamard, J. 253 286 288 289
Hadwiger, H. 85
Halmos, P. 205
Hamilton, Sir W.R. 258
Hano, J. 355
Harmonic vector 354
Hazzidakis, J.N. 237
Heine — Borel theorem 5
Helicoid 204
Helix 160
Helix, circular 157
Herglotz, G. 39
Hermitian matrix 109
Higher-order connection 357
Hilbert, D. 280
Holonomy group, homogeneous 320
Holonomy group, local 323
Holonomy group, nonhomogeneous 327
Homeomorphism 2
Homomorphism 87 110
Homothety, riemannian 345
Hopf, E. 352
Hopf, H. 213 250 255 260 283n. 286 289
Horocycle 278
Hull, convex 250
Hurwitz, A. 253
Huygens, C. 40 72
Hyperbola 13 34
Hyperbolic affine curvature 294
Hyperbolic circle 277
Hyperbolic cosine theorem 279 281
Hyperbolic geometry 275
Hyperbolic paraboloid 168 302
Hyperbolic point 213 291
Hyperbolic rotation 277
| Hyperbolic sine theorem 279
Hyperbolic spiral 13 61
Hyperbolic translation 278
Hyperboloid 302
Hyperosculating conic 151
Hypersurface, local 196
Hypocycloid 61
Hypotrochoid 71
i frame 315 357
Ideal 113
Identity, Bianchi 325 359
Identity, Jacobi 112
Image, spherical 212
Image, tangent 19
Impulsion, instantaneous 57
incircle 82
Independence, linear 175
Index raised, lowered 315
Indicatrix, Dupin’s 215
Indicatrix, normal 161
Indirect similitude 60
Inequality, Cauchy 9
Inequality, isoperimetric 83
Inequality, triangle 17
Infinitesimal connection 357
Infinitesimal rigidity 246
Infinitesimal vector 104
Infinity, point at 90 225
Inflection 5 152
Inner automorphism 111
Inradius 83
Instantaneous impulsion 57
Integrability, condition of 230
Integrability, total 242
Integral curvature 284
Integral curvature, absolute 285
Integral invariant 144
Integral of matrix 10
Invariant 117 135
Invariant connection 360
Invariant derivative 233
Invariant subset 113
Invariant, differential 139
Invariant, general affine 153
Invariant, geometric 138
Invariant, integral 144
Invariant, k-point 137
Invariants, complete set of 144
Inverse 86
Inverse movement 70
inversion 224
Involute of circle 25
Isochrone 76
Isomer 186
Isometric surfaces 212
Isometry 272
Isomorphism 87
Isoperimetric deficit 85
Isoperimetric inequality 83
Isothermal coordinates 246
Isothermal surface 247
Isotopic congruence 259
Jacobi equation 285
Jacobi identity 112
Jacobi, C.G.J. 288
Jacobian 104
Jacobson, N. 124
Jerrard, R. 26
Jessen, B. 253
jet 361
Joachimsthal, F. 222 228 268
Jordan curve 4
k-form 187
k-form, differential 189
k-point geometry 138
k-point invariant 137
k-vector 187
Kawaguchi connection 361
Kernel 114
Kernel-index notation 177
Kervaire, M., I97n. 205
Killing vector 272 342
Killing, W. 112 272 289 341
Klein geometry 139
Klein, F. 102 154
Knebelman, M.S. 357 362 363
Kneser, A. 48 51 52 54
Knotted curve 255
Kobayashi, S. 345 354 363 364
Kronecker symbol 104
Kronecker symbol, generalized 186
Kuiper, N.H. 280 289
La Hire, P. de 69 72
La Hire’s circle 69
Laguerre, E. 342
Laplacean 329
Left translation 89
Left-hand derivative 17
Leibniz, G.W. von 74w.
Lemniscate 13 43
Length 9 262
Length of normal 12
Length of tangent 12
Length, total 15
Levinson, N. 118
Lichnerowicz, A. 355 364
Lie algebra 106 112
Lie derivative 126 127
Lie differential equation 116
Lie product 105
Lie quadric 312
Lie, S. 102 103 139 147 148 154 227 229
Liebmann, H. 252
Lie’s fundamental theorem, first 130
Lie’s fundamental theorem, second 128
Lie’s fundamental theorem, second, converse of 130
Lie’s fundamental theorem, third, converse of 112
Line elements 49 52
Line elements, concircular 52
Linear connection 357
Linear independence 175
Lines, asymptotic 226
Lines, contour 310 311
Lines, projective 90
Lines, straight 59 143 152
Liouville metric 270
Liouville, J. 225 270
Local subspace 196
Local surface 196
Local transitivity 135
Locher-Ernst, L. 14
Locus, nodal 47
Logarithmic spiral 7 17 59
L’Hospital, G.F. de 70
MacDuffee, C.C. 346n.
MacKenzie, R.E. 205
MacLaurin’s spiral 13 25 34
MacLaurin’s trisectrix 13
Malus, E.L. 259
Manifold,  196
Manifold, compact 197
Manifold, Riemannian 314
Map,  4
Map, area-preserving 247
Map, conformal 224 247
Map, geographic 247
Map, projection 201 262
Map, transpose 180
Maschke, H. 310
Matrix, bounded 22
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