Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Hertrich-Jeromin U. — Introduction to Mobius Differential Geometry
Hertrich-Jeromin U. — Introduction to Mobius Differential Geometry

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Introduction to Mobius Differential Geometry

Автор: Hertrich-Jeromin U.

Аннотация:

Hertrich-Jeromin introduces students to the geometry of surfaces and submanifolds in the conformal sphere using various models. He starts with "the Reimannian point of view" and proceeds to the projective model (with a brief description of sphere congruences and their envelopes) and two applications, the first for conformally flat hypersurfaces and the second for isothermic and Willmore surfaces. He continues by describing a quaternionic model and application and a Clifford algebra model and application, thoughtfully providing the classical model of Möbius geometry in table form for reference.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 1st edition

Год издания: 2003

Количество страниц: 413

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$D_{\lambda}$-pair      217
1-parameter group      230 379
2-orthogonal system      190
2-plane      174
2-sphere      169ff
2-sphere congruence      168f 175
3-sphere      305
Absolute quadric      36 43 155
Adapted frame      56ff 162 165 297 321ff 344f 351
Adjoint action      286
Adjoint representation      287
Affine sphere complex      121
Almost complex structure      19
Alternions      280
Angle of intersection      39 291f
Antipodal map      52
Antipodal points      42
Approximation result      382
Archimedes — Lambert projection      15
Associated family      235 378f
Associated family of minimal surfaces      120
Bending energy      125 144
Bianchi's permutability theorem      246ff 361
Blade      279
Blaschke's problem      6 104 106 375
Bonnet's theorem      100
Boundary geometry      47
Branched channel hypersurface      66 68 70f
C-pair      195
Calapso potential      193 231
Calapso transformation      113 185 227ff 267 368 370 379
Cart an tensor      72
Cartan geometry      381
Cartan — Moore lemma      76
Cartan's theorem      71 84
Catenoid      142 201 213
Catenoid cousin      275
Cauchy problem      353f
Cayley — Hamilton identity      106
Center curve      145
Center of a hypersphere      37
Central projection      49
Central sphere congruence      80 102 120ff 130f 233 252 329ff 371f
Channel hypersurface      62
Channel surface      62ff 67 95 104 132ff
Christoffel pair      117f 185 195 363
Christoffel transformation      118 185 193f 264 362f
Christoffel's problem      6 104 115ff 194 335
circle      31
Circle congruence      94
Circle packing      383
Circle pattern      383
Circular cone      64f
Circular curvature lines      67
Circular cylinder      64f
Circular lattice      335 349
Circular net      350
Circular torus of revolution      64 66
Clifford algebra      149 277 280f 283 301 303 308
Clifford algebra model      5
Clifford conjugation      283 310
Clifford dual      288f 319
Clifford group      284f 310 316
Clifford multiplication      304 308
Clifford product      277 280f 309
Clifford torus      66 124 142 224 239 241
Codazzi equations      23 58 163
Codazzi tensor      20
Collineation      43
Compatibility conditions      23 57ff 162f 297f 325 339f 348 351
Completely integrable      216
Complex coordinates      19
Complex structure      19 172
Cone      64 135 141
Conformal 4-sphere      156 164
Conformal coordinates      18
Conformal curvature line coordinates      109 189 198 362 365
Conformal curvature tensor      18
Conformal deformation      104 113 185
Conformal diffeomorphism      52
Conformal equivalence      14
Conformal factor      14
Conformal fundamental form      26
Conformal fundamental forms      78f 81 83
Conformal Gauss map      26 102 120 122 193 233
Conformal geometry      52
Conformal Hopf differential      192f 231
Conformal invariants      24ff
Conformal map      14
Conformal metric      26 72 77 79 122
Conformal parameters      191
Conformal product hypersurface      87f
Conformal ra-sphere      16 38 50
Conformal rectangle      179f 261
Conformal second fundamental form      25
Conformal sphere      16
Conformal square      180
Conformal structure      15 50
Conformally equivalent metrics      14 49
Conformally flat      18 29
Conformally flat hypersurface      5f 68ff 78 83
Conformally minimal surface      103 123f 126
Congruence of 2-spheres      168f 175
Congruence of circles      75 93
Conjugate parameters      190f
Connection form      57ff 162f 297ff 324f
Constant Gauss curvature      88 98 100
Constant mean curvature      98 100 114 118 121 130 186 196 218ff 243 250
Constant sectional curvature      15
Contact element      41 290 296 327 329 331
Covariant derivative      58f
Cross-ratio      175f 179ff 248 261 292ff 332f 359
Curvature direction      28 107
Curvature line coordinates      85 190f 338
Curvature lines      231
Curvature sphere      60f 67
Curvature sphere congruence      233
Curvature tensor      16 59
Curved flat      69 74 76f 111f 228 234f 336 372 376ff
Curvilinear coordinates      337
Cyclic Guichard net      69 89 95ff
Cyclic system      75ff 93ff
Cylinder      63 135 141
Darboux pair      110f 185 217 334 372
Darboux sphere congruence      110
Darboux transformation      104 110 131 185 213 216f 266 336 372f
Demoulin family      335 356ff
Dini's helix      89ff
Discrete 1-form      263
Discrete catenoid      276
Discrete circular net      350
Discrete cone      355
Discrete curvature line net      260f 350
Discrete cylinder      355
Discrete Gauss map      274
Discrete holomorphic net      274
Discrete hyperbolic Gauss map      275
Discrete isothermic net      7 147 186 259ff 383
Discrete k-sphere congruence      349
Discrete Maurer — Cartan equation      348
Discrete net      261
Discrete net theory      7 382
Discrete orthogonal net      7 345
Discrete orthogonal system      334f 345ff
Discrete Ribaucour congruence      266 350
Discrete sphere curve      355
Discrete structure equations      345
Discrete surface      355
Distance sphere      24 29
Dual space      151 177
Dual surface      117 123
Duality      104 273
Dupin cyclide      27 64 241
Dupin's theorem      87 334 338f
Eigendirection      151
Eigenvalue      151
Eigenvector      151
Elastic curve      125 140 144
Elastic energy      102
Elastic force      102
Elastic surface      102 126
Elasticity of membrane      125
Elementary 2-cell      348
Elementary k-cell      349 353
Elementary quadrilateral      348
Elements of Moebius geometry      3 35
Ellipsoid      202
Elliptic function      96
Elliptic geometry      52
Elliptic hyperplane      42
Elliptic sphere complex      42
Elliptic sphere pencil      40 168 173
END      204
Enneper cousin      256 259
Enneper surface      257
Envelope      53ff 165ff 175 294ff 326ff 350
Enveloping conditions      54 56 167 175 294ff
Equivariant minimal surface      143
Equivariant surface      137
Essential Moebius transformation      208 366
Euclidean frame      323
Euclidean hyperplane      42
Euclidean n-space      301 309
Euclidean space      42 47 53
Euler — Lagrange equation      129
Extended Gauss map      111
Exterior algebra      277 279ff
Exterior product      309
Filtered algebra      281
Fixed point      318
Fixed point set      170
Flat (in a symmetric space)      74
Flat light cone immersion      71
Flat normal bundle      31 71 94 107 130 338
Fractional linear transformation      146 158 316
Free elastic curve      141
Fubini-Study metric      37 51
Fundamental theorem      24
Fundamental theorem of projective geometry      45
Gauge transformation      60 162 165 323f
Gauss curvature      17
Gauss equation      23 58
Gauss map      53
Gauss — Ricci equations      162
Generalized Gauss map      73 76
Generating sphere      62
Generic hypersurface      78
Geodesic curvature      145
Geometric algebra      277 279ff 288
Geometric method      382
Goursat transformation      185 205ff 265 365f
Graded algebra      279
Grassmann algebra      277 279ff
Grassmannian      168 300
Great sphere      42
Group homomorphism      158
Guichard net      69 86
Harmonic Gauss map      124
Harmonic map      126
Harmonic separation      43 180
Hexahedron lemma      182 249 266 270
Hill's equation      238
Hodge dual      289 303
Hodge-* operator      289
Holomorphic function      197f 200 209 212 223 237
Holomorphic quadratic differential      198f 218 364f 369 374
Homogeneous coordinates      36 146 153ff 277 306 308
Homogeneous space      73 111 161 164 234 321 324
Hopf differential      115 117 191 198 200 365
Horospherical net      187 260 273 275
Horospherical surface      119 131 245 250ff 274
Hyperbolic Gauss map      131 252
Hyperbolic geometry      52
Hyperbolic hyperplane      29 42
Hyperbolic space      15 42 47 53 119 131 187 245 250 274
Hyperbolic sphere complex      42
Hyperbolic sphere pencil      41
Hyperplane      42 50f
Hypersphere      28 31 35 156 288 318
Imaginary rotation      213
incidence      38 156 318 320
Incidence plane      42
Induced conformal structure      25 231
Induced covariant derivative      23
Induced metric      58f
Infinity boundary      42 48f
Inner product      280
Inner space      42
Integrable system      1 6f 103f 111 184 228 334f
Intersection angle      39 291f
inversion      43 46 307 317
Involution      46f 50f 169f 305 318ff
Isometry group      51
Isothermal coordinates      19
Isothermal lines      103
Isothermic channel surface      132 135
Isothermic immersion      200
Isothermic net      261
Isothermic surface      6 102 109ff 130 138 147 184ff 189f 334f 361ff
Isotropic normal field      55
Isotropy algebra      73 164
Isotropy group      74 161 164 321 323
Jacobi elliptic function      91 202
Jacobi identity      283
Joachimsthal's theorem      29
k-vector      279
Killing metric      77
Klein model      47
Klein's Erlanger program      2 33
Koszul's identity      338
Kulkarni — Nomizu product      16
Lame function      85 338
Lame's equations      82 87 334 340
Laplacian      330
Lawson's correspondence      114 243 250
Levi-Civita connection      16 23 338
Lichtenstein      19
Lie algebra      283 320
Lie algebra isomorphism      159
Lie sphere geometry      361 380
Light cone      37 155
Light cone immersion      59
Linear sphere complex      41 44 50f 174
Linear Weingarten surface      69 97ff
Linearization of Moebius geometry      33
Lines of equal temperature      103
Liouville's theorem      32 52
Lorentz group      43
Lorentz sphere      37 55
Lorentz transformation      46 51
m-orthogonal system      342
m-sphere      41 319
Master Christoffel transformation      211 229 265
Matrix multiplication      308
Maurer — Cartan equation      57ff 162 297 325 339 348 351
Mean curvature      102
Mean curvature sphere      102 121
Mean curvature sphere congruence      121 329ff 371
Mean curvature vector      329
Mercator map      15
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте