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Guggenheimer H.W. — Differential Geometry

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Название: Differential Geometry

Автор: Guggenheimer H.W.

Аннотация:

This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 378

Добавлена в каталог: 16.12.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$C^{n}$ map      4
$C^{r}$ manifold      196
$C^{r}$ structure      197
$GL_{n}$       95
$K^{n}$ curve      5
$O^{*}_{3}$       98
$O_{2}$       87
$O_{n}$       98
$R_{2}$       147
$SL_{2}$       147
$SL_{n}$       98
$Sp_{2}$       110
$Sp_{n}$       110
Abelian multiplication      86
Action, effective      129
Aczel, J.      154
Admissible frame      356
Ado, I.      113 120
Aeppli, A.      256
Affine arc length      149 170
Affine curvature line      310
Affine curvature, elliptic      292
Affine curvature, Gauss      310
Affine curvature, hyperbolic      294
Affine curvature, mean      310
Affine curvature, plane      150 172
Affine evolute      153
Affine fundamental form      297 298
Affine geodesic      309 311
Affine normal      151 292 293 299
Affine parameter      336 359
Affine principal direction      310
Affine sphere      301 306
Affine tangent normal      309
Affinity, central      95
Affinity, normal      95
Affinity, riemannian      345
Aleksandrov, A.D.      253 259
Alexandroff, P.      283n.
Algebra      103
Algebra, derived      114
Algebra, Grassmann      188
Algebra, Lie      106
Algebra, Lie, abstract      112
Algebra, reductive      129
Algebra, semisimple      114
Algebra, simple      116
Algebra, tensor      184
angle      9 262
Angle defect      283
Angle, dual      165
Angle, Euler      99
Antipode      98
Apolarity      298
Apostol, T.M.      37n.
Appolonius      47
Arc length      15 156
arc length, affine      149 170
Arc length, affine surface      309
Arc length, element of      202
Archimedes, spiral of      13
Arcwise connectedness      322
Aronhold, S.      71
Astroid      17 45 61
Asymptotic direction      213 295
Asymptotic lines      226
Atlas      197
Atlas, maximal      203
Auslander, L.      205
Automorphism, inner      111
Autoparallel curves      329
Beltrami, E.      247
Berger, M.      354
Bernoulli, John      76 85
Bertrand curve      160
Bertrand, J.      158
Berwald, L.      174 354
Bianchi identity      325 359
Bianchi, L.      154 160 238 248 259 281 343 349 354
Biangle, geodesic      286
Bilinear function      181
Blaschke, W.      72 155 162 174 255 308
Bliss, G.A.      85 266 270
Bobillier, M.      72
Bochner, S.      351 352 353 355
Boltyanskii, V.G.      85
Bolzano property      27
Bonnesen, T.      85
Bonnet, O.      247
Bouligand, G.      14
Bounded matrix      22
Bounded variation      17
Bourbaki, N.      110 124 205
Brachistochrone      73 76
Buck, R.C.      5n. 105n.
Canonical coordinates      119
Caratheodory, C.      34
Cardioid      13
Carleman, T.      154 155
Cartan map      108
Cartan matrix      10
Cartan, E.      10 113 139 147 148 154 188 205 238 246 247 260 340 349 354 361
Cartesian coordinates, geodesic      269 332
Catenary      25 46 61
Catenoid      205
Cauchy inequality      9
Cauchy sequence      285
Cayley, A.      47
Cayley’s surface      306
Center      114 120 123
Center surface      215
Centers, line of      215
Central affinity      95
Central plane      221
Central point      258
Central projection      255
Central section      221
Central surface      259
Cesaro, E.      72
Chart      197
Chern, S.S.      253 260 329 341
Chevalley, C.      124
Christoffel symbol      317
Christoffel, E.B.      253
Circle, geodesic      271
Circle, hyperbolic      277
Circle, involute of      25
Circle, La Hire’s      69
Circular helix      157
Clairaut differential equation      44
Clairaut, A.      267
Clifford parallel      282
Clifford, W.K.      101
Closed curve      3
Closed surface      197
Coddington, E.A.      118
Codifferential      329
Cohn-Vossen, S.      289
Commutator      106
Compact manifold      197
Complete space      285
Complete surface      285
complex numbers      93
Conchoid of Nicomedes      13
Concircular line elements      52
Cone, tangent      169
Conformal map      224 247
Conformal transformation      224
Conformal Weyl tensor      337
Congruence of revolution      259

Congruence, isotropic      259
Congruence, line, principal direction of      257
Congruent curves      21
conic      64 151 152
Conic, evolute of      70
Conic, hyperosculating      151
Conjugate diameter      97
Conjugate families      216
Conjugate point      265
Connected set      147
Connectedness, arcwise      322
Connection, Cartan — Finsler      362
Connection, higher-order      357
Connection, infinitesimal      357
Connection, invariant      360
Connection, Kawaguchi      361
Connection, linear      357
Connection, tensor      363
Connection, transformed      360
Conoid      215
Constantinescu, C.      353 354
Contact of curves      28
Contact transformation      142
continuous curve      2
Continuous matrix      22
Contour line      310 311
Contraction      182
Convex hull      250
Convex surface      249
Convexity      5
Convexity, parabolical      154
Coordinate system      200
Coordinate tensor      182
Coordinates, canonical      119
Coordinates, contravariant      315
Coordinates, covariant      315
Coordinates, Fermi      335
Coordinates, geodesic cartesian      269 332
Coordinates, geodesic polar      264
Coordinates, isothermal      246
Coordinates, normal      330
Coordinates, Pluecker      163
Coset      118
Cosine theorem, hyperbolic      279 28
Cosine theorem, spherical      271
Covariant coordinates      315
Covariant derivative      233 318
Covariant differential      318 358
Coxeter, H.S.M.      34 58
Cross product      see “Vector product”
Cross ratio      146
Crudeli, U.      270
Curvature      see “Affine curvature” “Reimann
Curvature element      50 52
Curvature line      210
Curvature line, affine      310
Curvature of space curve      157
Curvature of space curve, jth      160
Curvature radius      20
Curvature radius, principal      253
Curvature, enforced      339
Curvature, euclidian plane      20 143
Curvature, euclidian plane, left-hand      27
Curvature, euclidian plane, mean      34
Curvature, Gauss      212 342
Curvature, integral      284 285
Curvature, mean      212 341
Curvature, normal      207
Curvature, point      336
Curvature, principal      210 214 338
Curvature, spherical      162
Curve representation      55
Curves of striction      166
Curves, $C^{n}$       4
Curves, $K^{n}$       5
Curves, autoparallel      329
Curves, Bertrand      160
Curves, closed      3
Curves, congruent      21
Curves, contact of      28
Curves, continuous      2
Curves, cycloidal      71
Curves, dextrorse      170
Curves, equidistant      278
Curves, euclidean      28
Curves, Jordan      4
Curves, knotted      255
Curves, not differentiate      7
Curves, Peano      1 3 7
Curves, podal      13
Curves, rectifiable      16
Curves, simple (Jordan)      4
Curves, sinistrorse      170
Curves, spherical      161
Cusp      5 41
Cusp locus      47
Cycloid      5 25 34 61 66 68
Cycloidal curve      71
Cylinder      197
Darboux direction      293
Darboux frame      210 293
Darboux umbilic      292
Darboux, G.      16 161 228 229 259
Deficit, isoperimetric      85
Deformation, pure      95
Dented gears      62 71
Derivative, covariant      233 318
Derivative, invariant      233
Derivative, left-hand      17
Derivative, Lie      126 127
Derivative, matrix      8
Derivative, right-hand      17
Derivative, Schwarzian      146
Derived algebra      114
Determinant      65 188
Developable      167
Development      263 326
Dextrorse curve      170
Diameter      153
Diameter, Conjugate      97
Differentiability condition, natural      144
Differential equation, Clairaut      44
Differential equation, Lie      116
Differential form      179
Differential invariant      139
Differential parameter      329
Differential vector      199
Differential, covariant      318 358
Differential, exterior      189
Differentiation, dot      8
Differentiation, prime      8 15
Dilatation      58
DIMENSION      175
Dini, U.      169 237
Direct product      91
Direction, Darboux      293 (see also “Principal direction”)
Distance      285
Distribution parameter      169
Dot differentiation      8
dragging      126
Dry friction      56
Dual angle      165
Dual numbers      163
Dual sphere      164
Dual vector      164
Dupin, C.      216 223 259
Dupin’s indicatrix      215
e frame      315 356
Edge of regression      167
Effective action      129

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