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
Aleksandrov A.D., Zalgaller V.A. — Intrinsic Geometry of Surfaces
Aleksandrov A.D., Zalgaller V.A. — Intrinsic Geometry of Surfaces



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Intrinsic Geometry of Surfaces

Авторы: Aleksandrov A.D., Zalgaller V.A.

Аннотация:

Alexandrov's contribution to the field of intrinsic geometry was both original and extremely influential. This volume consists of an original core of classic material, originally published in Russian in 1948, with additional supplementary material making it of particular current interest. It begins with an outline of the main concepts and results and then covers topics including general propositions on an intrinsic metric; characteristic properties of the intrinsic metric of a convex surface; angles and curvature; existence of a convex polyhedron with prescribed metric; curves on convex surfaces and the role of specific curvature. This book provides definitive sources for the development of intrinsic geometry. A classic in the field that remains unsurpassed in its clarity and scope, this text would be of great value to graduate students seeking a better understanding of this area of geometry.


Язык: en

Рубрика: Математика/Геометрия и топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1967

Количество страниц: 327

Добавлена в каталог: 16.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Additivity of angle      22
Additivity of area, complete      261
Additivity of curvature      154
Additivity of curvature, complete      154
Additivity of length      2
Additivity of rotation      187
Additivity of rotation, complete      272—273
Additivity of sector      117
Adjacent angles      22
angle      4—5 20
Angle, and direction      23—24 178
Angle, and distance up to a curve      129
Angle, and distance up to a shortest arc      27 29
Angle, complete around a point      45—46 67 117—118
Angle, extended      313
Angle, in the strong sense      28 127—128 314
Angle, in the weak sense      310—311
Angle, its existence      34—39 42 113—116
Angle, lower      20 249
Angle, lower, strong      28—29 33 314
Angle, of a sector      45 116—117
Angle, of a sector, its finiteness      122
Angle, on the side of the sector      126
Angle, upper      5 20—27 309
Angle, upper, strong      314
Approximation by polygonal curves      276
Approximation by polyhedra      9 79
Approximation by Riemann metrics      9
Approximation by shortest arcs      190
Area      11 15—16 260—261 263
Area of a point, polygon      261
Area of a polygon      258—259
Area of a spherical representation      17
Area of a triangle      11 255 258
Boundedness of the absolute curvature of approximating metrics      122
Caratheodory measure      146
Charges      231—232
Charges, their positive and negative parts      232
Circumference      16
Compactness of a set of curves      3
Compactness, weak      233
Comparison with the angle of a plane triangle      11 31—32 71—72 176 214 218
Comparison with the area of a plane triangle      11 255 258
Completion of a space      201—203
Condition of bounded curvature      6
Connectedness, metric      3
Convergence of angles      251—252
Convergence of areas of polygons      265
Convergence of curves      3 220 224 294—304
Convergence of figures in converging spaces      223
Convergence of induced metrics      227
Convergence of length      283
Convergence of metrics      9 222
Convergence of metrics, locally uniform      222
Convergence of metrics, nonuniform      91
Convergence of points      1
Convergence of polygons      220 223 225
Convergence of sector angles      237 248—249
Convergence of sectors      221 223
Convergence of spaces      222
Convergence, weak      232—233
Convergence, weak, local      234
Convergence, weak, of areas      267
Convergence, weak, of the curvature      238—239
Convergence, weak, regular      242 244
Convexity      48
Convexity, absolute      49
Convexity, fully      49
Convexity, relative      76
Convexity, relative to the boundary      6 48
Covering by triangles      59
Curvature      145 154
Curvature, absolute      154 160
Curvature, absolute, of converging polyhedral metrics      122
Curvature, and excess of a polygon      166—175 212—213
Curvature, and excess of a triangle      213
Curvature, as a charge      234—235
Curvature, extrinsic      17
Curvature, in a polyhedral metric      8
Curvature, its positive and negative parts      151—152
Curvature, of a one-point set      10 130 163
Curvature, specific      15 17
Curvature, various definitions      154—155
Curve      2
Curve, parametrized      2
Curve, simple      2
Curve, with rotation of bounded variation      270 304—305
Cutting      12
Decomposition into triangles      61
Decomposition into triangles, regular and nonregular      145
Decomposition of a sector      121
Density of shortest arcs      119
Development, constructed with respect to a triangulation      69 243—244
Development, multidimensional      19
Development, of a polyhedron      8
Diameter of a triangle      253
Direction      23
Direction, and angle      178
Direction, in the extrinsic sense      17
Direction, in the intrinsic sense      23
Direction, its existence      273 297
Disc      16
Distance      1
Distance, up to a curve      129
Distance, up to a shortest arc      27 29
Euler’s theorem      63
Excess of a polygon      174 212—213
Excess of a triangle      31
Excess of a triangle and its curvature      212—213
Excess of a triangle with respect to the sector angles      65
Excess, relative, of a triangle      317
Excesses of nonoverlapping triangles      132—133
Excesses of nonoverlapping triangles, reduced      142
Excesses of triangles of a triangulation      63
Excision of a polygon      200
Extremal problems      15
Gauss — Bonnet theorem      8—9 190
Gauss’ Theorem      17
Geodesies      4 16
Identity of topologies      91
Isothermal coordinates      14—15
K-plane      308
Kolmogorov test for weak convergence      233 234
Length of a curve      2 15—16
Length of a curve and chord length      76 279—280
Lengths of converging curves      3 96 223 283
Linear element      14—15
Load, escaping or fleeing      233—234
Loop, enclosing a singular point      125
Loop, shortest      51
Manifold, two-dimensional with bounded specific curvature      17
Manifold, two-dimensional, of bounded curvature      6
Manifold, two-dimensional, with an edge      16—17 202
Metric      1
Metric, approximated by a polyhedron      90
Metric, complete      92
Metric, induced      3
Metric, intrinsic      3—4
Metric, polyhedral      7—8
Neighborhood, absolutely convex      51
Neighborhood, of a polygon      51 122
Neighborhood, with small perimeter      53
Nonlocal characteristics of the angle      314—315
Nonlocalness of the condition of boundedness of the curvature      65
Nonoverlapping      145
Nonoverlapping of triangles      6 50
Parallel translation      19
Parametrization of a curve      2
Pasting      13 205—206 286
Pasting of polygons      200
Point, cusp      306
Point, of a triangle, interior      50
Point, singular      118 281—282 305
Point, through which there pass shortest arcs      46—47
Polygon      12 201
Polygon with cuts      12 13
Quadrilateral, deformation      34—36
Quasigeodesic      16
Realization of a metric      18
Rectifiability of a curve      283
Rotation of a curve      184 270
Rotation of a curve and the curvature of the curve      186
Rotation of a curve and the curvature of the region      190
Rotation of a curve in polyhedral metric      8
Rotation of a curve in space      17
Rotation of a curve, its existence      184—185
Rotation of a curve, its positive and negative parts      8 271—272
Rotation of a curve, left and right      184
Rotation of a curve, proper      16
Rotation of shortest arcs      10 197
Sector      39—40 116
Semineighborhood of a curve      17
Semitangent      17
Shortest arc      4
Shortest arc, leftmost      40
Shortest arc, relative      76
Shortest arcs without superfluous intersections      51
Side of a curve      181—184 188—189 306
Space, boundedly compact      93
Space, compact      1—2
Space, complete      92—93
Space, fully normal      231
Space, locally compact      2
Space, metric      1
Space, of directions      23
Space, with curvature less than K      19
Surfaces, convex, generalized convex      17—18
Surfaces, metric disconnected      7
Surfaces, of bounded extrinsic curvature      18
Surfaces, represented by the difference of convex surfaces      17
Surfaces, with generalized second derivatives      18
Tangent cone      16
triangle      5 49—50
Triangle inequality      1
Triangle inequality for upper angles      20
Triangle, convex relative to the boundary      6
Triangle, geodesic      154
Triangle, homeomorphic to a disk      5—6
Triangle, inflatable      49
Triangle, normal      214
Triangle, on a K-plane      308
Triangle, simple      6
Triangle, with exterior tails      43 50
Triangle, with interior tails      50
Triangulation      58
Twist      16
Uniform closeness of $\gamma$ to $\alpha$      124—125
Variation, farther from a vertex      106—113 248—249
Variation, of the angle $\gamma$      29 96—106 246—248 317
Variation, of the charge      232
Variation, of the rotation of a curve      301
Variation, of the rotation of converging curves      301 303
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2021
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте