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Montiel S., Ros A. — Curves and Surfaces
Montiel S., Ros A. — Curves and Surfaces

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Название: Curves and Surfaces

Авторы: Montiel S., Ros A.

Аннотация:

This textbook presents some of the most relevant global results of classical differential geometry, relative both to the study of curves and that of surfaces. Topics include the Gauss map and the second fundamental form, the divergence theorem, global extrinsic geometry, rigid motions and isometrics, and the Gauss-Bonnet theorem.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 384

Добавлена в каталог: 30.04.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Alexandrov      172 187
Ampere      2
Arc length      1
Archimedes      161
Area      141
Bartels      2
Bernouilli, D.      1
Bernouilli, John      1 206
Bernouilli, Joseph      2
Bertrand      68
Bianchi      31
Binormal      2 14
Binormal line      22
Blaschke      172
Bonnet      182 204 276 296 302
Brower      108 116 118 161 288 310
Brunn      173 189 311 325
Brunn — Minkowski inequality      189 325
Catenoid      95 239
Cauchy      2 32 205
Chain rule      48
Chasles      68
Chern      156
Circumscribed circle      346
Clairaut      2 31 240
Cohn — Vossen      205 218
Comparison of curves      22
Comparison of lines and surfaces      111 112
Comparison of planes and surfaces      113
Comparison of surfaces      96
Cone      38 39
Congruence      207
Connected component      36
Crofton      312 343
Curvature, centre      21
Curvature, Gauss      68 77
Curvature, mean      68 77
Curvature, of a curve      1
Curvature, of a curve, in $\mathbb{R}^3$      14
Curvature, of a curve, plane      10
Curvature, radius      1
Curvature, total      330
Curve      3
Curve, convex      328
Curve, coordinate      35
Curve, integral      258
Curve, knotted      345
Curve, on a surface      42
Curve, p.b.a.l.      9
Curve, parallel      321
Curve, parametrized      313
Curve, periodic      314
Curve, regular      8
Curve, simple      38 313 318
Cylinder      37 44 71 80 95 225
Darboux      2 68 240
Darboux, trihedron      240
Degree between curves      365
Degree between surfaces      277
Degree, local      281
Dependence of parameters      149
Descartes folium      314
Diffeomorphism      43
Diffeomorphism, local      54
Differential      46 48
Diquet      241
Distance      239
Divergence      157 322
Divergence, on surfaces      184
Domain, inner      118 174
Domain, inner of a curve      320
Domain, outer      118
Domain, outer of a curve      320
Domain, regular      159
Dominated convergence      148
Dupin      2
Efimov      173
Ellipsoid      36 37 80 174
Equations, Darboux      240
Equations, Frenet      10
Euler      1 31 67 206 312
Euler, characteristic      295 302 304
Evolute      21
Evolvent      21
Existence and uniqueness, theorem of      17 227
Exponential map      230
Fary      312 345
Fenchel      312 342
Field, conformal on a sphere      292
Field, conservative      351
Field, non-degenerate      289 292
Field, normal      69 119
Field, on $\mathbb{R}^2$      322
Field, on $\mathbb{R}^3$      157
Field, on a surface      69
Field, tangent      69 257
First fundamental form      68 207
First integral      259
Flow of a field      258
Formula, area      152
Formula, Bertrand — Puiseux      241
Formula, change of variables      144
Formula, Crofton      343
Formula, Diquet      241
Formula, Gauss — Bonnet      296 302
Formula, Herglotz      217
Formula, integration in polar coordinates      147
Formula, length      321
Formula, Poincare — Hopf      302
Formula, variation of area      193
Formula, variation of length      222
Formula, variation of volume      194
Formulas, Frenet      16
Formulas, Green      351
Formulas, Minkowski      184
Four-petal rose      313
FOURIER      2
frenet      2 16
Frenet, dihedron      9
Frenet, trihedron      14
Fubini      146
Function, differentiable      40
Function, distance      41 87
Function, height      41 85 87 301
Function, implicit      36 49
Function, integrable      139
Function, inverse      58
Function, on a sphere      150
Function, support      94 177
Gauss      2 31 68 157 172 203 210 232 275 296 302
Gauss, Lemma      232
Gauss, map      68 76
Geodesic      1 223
Geodesic, ball      232
Geodesic, existence      228
Geodesic, homogeneity      229
Geodesic, minimizes locally      233
Germain      68
Gluck      313
Gradient      161
Gradient, on surfaces      197
Graph      35 53 71
Grauenstein      312 331
Green      157
Gromov      311
Group of isometries      209
hadamard      172 175 178 311
Hartman      173 273
Heintze      173 186
Heintze — Karcher’s inequality      186
Helein      311
Helicoid      91 239
Helix      4 16 19 22
Herglotz      205 217 312
hessian      85 87
hilbert      91 172
Hopf      206 238 312
Hurwitz      311
Hyperboloid      37 44
Index of a field      289
Index, rotation      329
Integral on $S \times \mathbb{R}$      137
Integral on a surface      139
Isometry      208
Isometry, local      207
Isoperimetric inequality in the plane      326
Isoperimetric inequality in the space      195
Jackson      312
jacobi      206
Jacobian      76 277
Jacobian, absolute value      57 136
Jacobian, on curves      368
Jellett      91 172 185
JORDAN      107 116 310 320
Karcher      173 186
Kelvin      135
Kneser      312
Kramer      31
Lagrange      205
Lancret      2 23
Laplace      2
Laplacian      351
Laplacian on $\mathbb{R}^3$      164
Laplacian on surfaces      197
Lashoff      156
legendre      275
Leibniz      1
Length of a curve      7
Length of a periodic curve      315
Length, arc      5 8
Liebmann      91 172 184 205
Liouville      206
Logarithmic spiral      9
Malus      2
Map, constant      41
Map, differentiable      40
Map, identity      41
Map, inclusion      41
Massey      173 273
Maxwell      135 311
Measure zero      126 131
Measure zero on a surface      142
Meusnier      2 68
Milnor      312 345
Minding      172 205 241
Minkowski      172 189 311 325
Moebius strip      71 74
Monge      1 31 67
monodromy      196
Monotone convergence      148
Mukhopadhyaya      312
Myers      182
Neighbourhood, coordinate      35
Neighbourhood, normal      236
Neighbourhood, tubular      122
Neighbourhood, tubular, of a curve      321
Newton      1
Nirenberg      173 273
Normal, line      8 319
Normal, of a curve, in the plane      9
Normal, of a curve, in the space      14
Normal, of a surface      46 51
Normal, sections      81
Oresme      1
Orientation      119
Orientation, of curves      319 320
Orientation, of surfaces      70
Orientation, preserving      76
Oriented distance      125
Osculating, circle      21
Osculating, plane      23
Osserman      313 346
Oval      328 329
Ovaloid      172 174
Ovaloid, intersection with lines      177
Pappus      311
Paraboloid      37 90 174 256
Paraboloid, hyperbolic      80
Parametrization      35
Parametrization, by curvature lines      261
Parametrization, change of      39 40
Parametrization, orthogonal      95 261
Partition of unity      143
Period of a periodic curve      314
Poincare      276 295 302
Point, critical      48
Point, elliptic      83 87
Point, hyperbolic      83 87
Point, of double intersection      115
Point, of first contact      115
Point, parabolic      83
Point, planar      83
Point, umbilical      83
poisson      2
Poncelet      2
Principal curvatures      78
Principal directions      79 84
Projection      125
Ptolemy      31
Puiseux      241
Quadric      37 80
Region of a surface      136
Regular value      36 111
Reilly      173
Reparametrization      8
Reparametrization by arc length      9
Riemann      32 239
Rigid motion      7 80 144 207
Rinow      206 238
Rodrigues      2 68
Rustihauser      312
Saint-Simon      68
Saint-Venant      2
Samelson      108 118 312
Sard      112 132 311 321
Schmidt      311
Schwarz      173
Second fundamental form      68 76 77 207
Second variation of the length      253
Segre      312
Senff      2
Separation, global      116
Separation, local      108
Serret      2
Sphere      36 45 71 79 143 145 213 292
Steiner      173
Stoker      172 175 178 273 311
Stokes      135 157 311
surface      32 34
Surface, convex      174
Surface, of revolution      55 163
Surface, orientable      70
Surface, oriented      70
Surface, parallel      123 145 147
Surface, star-shaped      57 95 177
Surface, strictly convex      175
Surface, triply periodic      56
Surface, umbilical      84
Surface, with parallel s.f.f.      263
Surfaces, congruent      207
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