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| Aleksandrov A.D., Zalgaller V.A. — Intrinsic Geometry of Surfaces |
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| 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 in the strong sense 28 127—128 314
Angle in the weak sense 310—311
Angle of a sector 45 116—117
Angle of a sector, its finiteness 122
Angle on the side of the sector 126
Angle, complete around a point 45—46 67 117—118
Angle, extended 313
Angle, its existence 34—39 42 113—116
Angle, lower 20 249
Angle, lower, strong 28—29 33 314
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 and excess of a polygon 166—175 212—213
Curvature and excess of a triangle 213
Curvature as a charge 234—235
Curvature in a polyhedral metric 8
Curvature of a one-point set 10 130 163
Curvature, absolute 154 160
Curvature, absolute, of converging polyhedral metrics 122
Curvature, extrinsic 17
Curvature, its positive and negative parts 151—152
Curvature, specific 15 17
Curvature, various definitions 154—155
Curve 2
Curve with rotation of bounded variation 270 304—305
Curve, parametrized 2
Curve, simple 2
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 of a polyhedron 8
Development, multidimensional 19
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
Parameterization 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
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 of directions 23
Space, compact 1—2
Space, complete 92—93
Space, fully normal 231
Space, locally compact 2
Space, metric 1
Space, with curvature less than K 19
Surfaces of bounded extrinsic curvature 18
Surfaces with generalized second derivatives 18
Surfaces, generalized convex 17—18
Surfaces, metric disconnected 7
Surfaces, represented by the difference of convex surfaces 17
Tangent cone 16
triangle 5 49—50
Triangle inequality 1
Triangle inequality for upper angles 20
Triangle on a K-plane 308
Triangle with exterior tails 43 50
Triangle with interior tails 50
Triangle, convex relative to the boundary 6
Triangle, geodesic 154
Triangle, homeomorphic to a disk 5—6
Triangle, inflatable 49
Triangle, normal 214
Triangle, simple 6
Triangulation 58
Twist 16
Uniform closeness of  to  124—125
Variation farther from a vertex 106—113 248—249
Variation of the angle , 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
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