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| Oprea J. — Differential Geometry and Its Applications |
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| Предметный указатель |
Line of curvature and developable surfaces 98
Line of curvature, as a geodesic 154
Line of striction 64
Line, parameterized line 1
Line, shortest distance in R3 7—8
Line, symmetry 239
Linear transformation 74
Linking number 23
Manifold 313
Maple 38 85 119 183 249 300
Mayer field 270
Mean curvature 87 325 334
Mean curvature and Euler's formula 90
Mean curvature and shape operator 88—89
Mean curvature in Maple 121
Mean curvature, as least surface area with fixed volume 141 293—294
Mean curvature, constant 115—116 139
Mean curvature, formula 89 91
Mean curvature, of Enneper's surface 94
Mean curvature, surfaces of Delaunay 115—116
Mean curvature, vector field 325 334
Mercator projection 183
Meridians 99
Meridians, as geodesies 152—153
Meromorphic 226
Metric (EFG) 64 91 168
Metric (EFG), in Maple 120
Metric (EFG), second fundamental form (Imn) 91 324
Metric (EFG), second fundamental form (Imn), in Maple 121
Minimal surface 90 128
Minimal surface adjoint 231
Minimal surface and compactness 112
Minimal surface harmonic 131
Minimal surface ruled 132
Minimal surface, as solution to Bjorling's problem 242
Minimal surface, Catalan's 134—135 228
Minimal surface, catenoid 59—60 114 228
Minimal surface, Enneper's 61 85 135
Minimal surface, equation of 130
Minimal surface, equation of, as Euler — Lagrange equation 265
Minimal surface, Henneberg's 134—135 229 231 241
Minimal surface, Henneberg's, as solution to Bjorling's problem 241
Minimal surface, Scherk's fifth 134
Minimal surface, Scherk's first 130
Minimal surface, Scherk's first, symmetry of 239—240
Minimal surface, second variation of 244
Minimal surface, versus area-minimizing 137—138
Moebius strip 67—68
Moebius strip in Henneberg's surface 242
Monge patch 56
Myers' Theorem 342
Newton's Aerodynamical Problem 299
Newton's Aerodynamical Problem, Newton's curve 3
Nodary 118
Nonorientable surface 67
Normal coordinates 331
Normal curvature 79 151
Normal to a surface U 66—70
Normal vector fields 317
Orientable 68
Orientable manifold 315—316
Orientable surface 68
Osculating circle 28
Parallel postulate 188
Parallel surface 92
Parallel transport 195 329
Parallel vector field 194 328
Parallel vector field and Foucault's pendulum 199
Parallel vector field, existence of 194
Parallels 99
Parameter curves 53
Patch (parameterization, chart) 54 312
Path connected 55
Plateau's problem 136
Pontryagin maximum principle 297
Pontryagin maximum principle in Maple 308—311
potential energy 265 284
Principal curvatures 81 90
Principal curvatures and Hilbert's Lemma 114
Principal curvatures, as eigenvalues of shape operator 87
Principal curvatures, as eigenvalues of shape operator of surface of revolution 101
Principal normal N 19
Pseudosphere 102—103
Pursuit curve 14
REcreate 48
Recreate3dview 49—50
Regular curve 16
Regular mapping 54
Reparameterization of curve 16 17
Ricci curvature 340
Riemann curvature 335—336
Ruchert's Theorem 248
Ruled surface 62
Ruled surface in Maple 85
Ruled surface minimal 132
Ruled surface, Gauss curvature of 97
Saddle surface 62 97
Scalar curvature 340
Schwarz reflection principle 239
Schwarz's inequality 6
Schwarz's theorem 245
Second fundamental form 91 324
Second fundamental form B(V,Z) 324
| Second fundamental form lmn 91—92
Second variation 244
Sectional curvature 337
Shape operator 71 322
Shape operator and Gauss curvature 87—89
Shape operator and mean curvature 87—89
Shape operator of cylinder 72
Shape operator of plane 72
Shape operator of sphere 72 323
Shape operator of torus 72
Shape operator, as symmetric linear transformation 76 323
Shape operator, eigenvalues of 76
Slope function 268
Sphere 57—58 67
Sphere, Gauss curvature of 91 95 108 357
Sphere, shape operator of 72 323
Spherical coordinates 57—58
Spiral of Cornu 38 281—282
Stereographic projection 170 233 313
Stereographic projection and area minimization 246
Striction, line of 64
Structure equation first 354
Structure equation second 355
Sturm — Liouville Theorem 217
surface 54
Surface area 128—129 189—190 262
Surface Catalan's 134
Surface catenoid 59—60 114
Surface cone 62 97—98
Surface cone lassoing 179
Surface cone, unrolling as Isometry 179
Surface cylinder 62 82 97—98
Surface cylinder unrolling 180
Surface Enneper's 61 93 134 229
Surface helicoids 60 97 178 182 228
Surface Henneberg's 134—135 229 231 241
Surface Henneberg's, with embedded Mobius strip 242
Surface of Delaunay 115 293
Surface of revolution 58 99
Surface of revolution, meridians and parallels of 99
Surface of revolution, principal curvatures 101
Surface, hyperbolic plane 170
Surface, hyperboloid of one sheet 63 97
Surface, hyperboloid of two sheets 95—96
Surface, Moebius strip 67—68 242
Surface, of revolution, Gauss curvature of 100
Surface, of revolution, least area 264
Surface, of revolution, minimal 114
Surface, Poincare plane 169 201
Surface, Richmond's 229
Surface, Scherk's fifth 134
Surface, Scherk's first 130 229
Surface, Scherk's first, symmetry of 239—240
Surface, sphere 57—58 67 108
Surface, stereographic sphere 170 176
Surface, tension 125—128 141
Surface, torus 60 100—101 171
Surface, unit normal (U) of 70 120
Suspension bridge 13
Symmetric matrix (transformation) 75 323
Symmetry line 239
Symmetry of Riemann curvature 338
Symmetry plane 239
Tangent developable 85 98
Tangent for nonunit speed curves  28
Tangent for unit speed curves T 18
Tangent plane 65
Tangent space 313
Tangent vector 3 53 65
Theorem Egregium 105
Torsion  21
Torsion of a nonunit speed curve 28—29
Torsion of a nonunit speed curve in Maple 41
Torsion , geodesic 195
Torsion , total torsion 24 80
Torsion , total torsion, of spherical curve 80
Torus 60
Torus, Gauss curvature of 100—101
Torus, shape operator of 72
Transition map 313
Trick 18
Twist 24
Umbilic 84 109
Umbilic on minimal surface 231
Undulary 118
Unduloid 118
Upper half-space 343
Vector field 70 193 317
Vector field and Bjorling's problem 238
Vector field parallel 194 328
Vector field parallel and Foucault's pendulum 199
Vector field, Lie bracket of 319
Velocity vector of curve 2
Viviani's curve 27 50—51
Weierstrass E-function 268
Weierstrass E-function for arclength integral 273—274
Weierstrass E-function, Weierstrass condition 272
Weierstrass — Enneper Representations 226
Weierstrass — Enneper Representations and area minimization 242—249
Weierstrass — Enneper Representations in Maple 249—250
Weingarten map 71
White's formula 24
Witch of Agnesi 12 43
Witch of Agnesi, whirling witch of Agnesi 163 186
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