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Alekseevskij D.V., Vinberg E.B., Solodovnikov A.S. — Geometry of Spaces of Constant Curvature
Alekseevskij D.V., Vinberg E.B., Solodovnikov A.S. — Geometry of Spaces of Constant Curvature



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Название: Geometry of Spaces of Constant Curvature

Авторы: Alekseevskij D.V., Vinberg E.B., Solodovnikov A.S.

Аннотация:

This book contains a systematic and comprehensive exposition of Lobachevskian geometry and the theory of discrete groups of motions in Euclidean space and Lobachevsky space. The authors give a very clear account of their subject describing it from the viewpoints of elementary geometry, Riemannian goemetry and group theory. The result is a book which has no rival in the literature. Part I contains the classification of motions in spaces of constant curvature and non-traditional topics like the theory of acute-angled polyhedra and methods for computing volumes of non-Euclidean polyhedra. Part II includes the theory of cristallographic, Fuchsian, and Kleinian groups and an exposition of Thurston's theory of deformations. The greater part of the book is accessible to first-year students in mathematics. At the same time the book includes very recent results which will be of interest to researchers in this field.


Язык: en

Рубрика: Математика/Геометрия и топология/Дифференциальная геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 254

Добавлена в каталог: 22.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abels, H.      159
Absolute      29
Adjacency transformation      160
Aleksandrov, A.D.      112 159
Allendoerfer, C.B.      122
Andreev, E.M.      106 111 112 204 237
Angle of a polyhedron at a face      120
Angle of parallelism      67
Angular excess      62
Angular measure of a cone      113
Angular measure of a cone, relative      120
Apanasov, B.N.      173
Axiom of maximum mobility      11
Axis of motion      94
Baer, R.      194
Bernoulli, J.      122
Bianchi, L.      220
Bieberbach, L.      151 170 174
Bolyai, J.      87
Bonnet, O.      63 122
Borcherds, R.      224
Boundary element of a planar group      187
Boundary of a homogeneous domain      29
Bravais, A.      180
Canonical system of generators of a planar group      186
Cauchy, A.      111
Centre of a parabolic translation      96
Chabauty topology      191
Chabauty, C.      191
Charlap, L.      181 182
Circular transformation      36
class      178
Class, arithmetic      178
Class, conformal (of a metric)      39
Clifford translation      94
Clifford, W.K.      94 133 156
Closure of a homogeneous domain      29
Cocycle      1—177
Collineation      29
Commensurable groups      150
Commensurator      238
Cone, director      113
Cone, dual      113
Continuation of a motion, canonical      92—93
Convex hull      57
Convex set      23
Cosine law      65
Cosine law, dual      65
Covolume of a discrete group      239
Coxeter, H.S.M.      112 125 198 201 214
Criterion of arithmeticity of a reflection group      226
Criterion of geometrical finiteness      172
Crystal structure      153
Curve, homogeneous      74
de Sitter, W.      135
Decomposition      146
Decomposition, compatible with a subspace      78
Decomposition, homogeneous      167
Decomposition, Iwasawa      98
Decomposition, normal      159
Defining subspace (of a plane)      22
Dehn — Thurston surgery      235 237
Dehn's twist      195
Dehn, M.      195 235
Delone, B.N.      182
Determinant of a scheme      201
Developable hypersurface '      133
Direction of parallelism      52
Dirichlet domain      148
Dirichlet, P.G.L.      148 173
Distance      26
Domain, fundamental (of a discrete group)      146
Domain, homogeneous      29
Dyck, W.      204
Efremovich, V.A.      231
Equidistant curve      73
Equidistant hypersurface      86
Euclid      6
Euler characteristic of a planar group      187
False faceting      159
Family of half-spaces, acute angled      106
Family of hyperplanes, indecomposable      108
Family of hyperplanes, non-degenerate      108
Family, locally finite      144
Fedorov, E.S.      155 180
fibonacci      167
Field of definition of an arithmetic group      218
Flag of a polyhedron      211
Formula, Gauss — Bonnet      63 122
Formula, Lobachevskij      125
Formula, Poincare      120
Formula, Riemann — Hurwitz      188
Formula, Schlaefli      119 121
Free action of a group      145
Fricke, R.      156
Frobenius, G.      109 219
Function, convex      27
Function, displacement      93
Function, Lobachevskij      123
Galois covering      184
Galois, E.      184
Garland, H.      232
Gauss, C.F.      63 122
General position, points in      22
Glide along a plane      92
Glide-reflection      71
Gram matrix of a convex polyhedron      105
Gram, J.P.      79 104
Gromov, M.      228 232
Group of compact type      187
Group of finite type      186
Group of motions      9
Group of motions, arithmetic of simplest type      218
Group of motions, arithmetic of the space $L^2$      219
Group of motions, arithmetic of the space $L^3$      220
Group of motions, arithmetic of the space $L^3$, universal      158
Group of motions, arithmetic of the space $L^7$      222
Group of motions, arithmetic of the space $L^n$      221
Group of motions, crystallographic of the space $E^n$      174
Group of motions, crystallographic of the space $L^n$, arithmetic      156
Group of motions, crystallographic of the space $L^n$, non-arithmetic      231
Group of motions, crystallographic of the, reflective      222
Group of motions, crystallographic, split (symmorphic)      177
Group of motions, discrete      144
Group of motions, discrete arithmetic      156
Group of motions, discrete crystallographic      145
Group of motions, discrete geometrically finite      168
Group of motions, discrete of compact type      169
Group of motions, discrete of divergent type      232
Group of motions, discrete uniform      145
Group of non-compact type      187
Group, $H^1$ cohomology      177
Group, arithmetic      222
Group, Bravais      180
Group, diaonal      98
Group, dihedral infinite      77
Group, discrete irreducible      98
Group, discrete reducible      98
Group, discrete reflection      200
Group, elementary      169
Group, finite      176
Group, Galois (of a covering)      184
Group, isotropy      8
Group, Kleinian      144
Group, Lanner      205
Group, Lie (of transformations)      8
Group, linear algebraic      98
Group, maximal      197
Group, modular      192
Group, of the first kind      190
Group, of the second kind      190
Group, planar      186
Group, Puchsian      183
Group, quasi-algebraic      98
Group, quasi-Lanner      205
Group, reductive      98
Group, reflection      198
Group, uniformization      185
Group, unipotent      98
Half-plane      23
Half-space      23
Helling, H.      167
Herglotz, G.      131
Hilbert's 18th problem      180
Hilbert, D.      6 180
Holohedry (syngony)      180
Holohedry, arithmetic      180
Honeycomb      215
Horocylce      74
Horosphere      87
Hyperplane      22
Hypersurface, standard      85
Inertia index of a scheme      201
Involution of a Riemann manifold      20
Isometry      9
Isomorphism of a homogeneous space      15
Isotropy representation      8
Iwasawa, K.      98
Jorgensen's inequality      170
Jorgensen, T.      167 170
Karpelevich, F.I.      103
Kazhdan, D.A.      170
Kerckhoff, S.P.      197
Killing, W.      156
Kim, A.C.      167
Klein, F.      32 156 208
Koebe, P.      46 196
Lambert, J.H.      67
Lanner, G.      204
Leech lattice      224
Leech, J.      224
Lemma, Margulis      170
Lemma, Selberg      151
Lie, S.      8
Limit point, conical      172
Limit point, cuspidal      172
Limit point, parabolic      163
Limit point, quasi-parabolic      163
Limit set      169
Line      22
Lines, divergent      51
Lines, parallel in the sense of Lobachevskij      52
Liouville, J.      39
Lobachevskij, N.I.      6 87 113 117 122 126 130
Lobell, F.      158 204
Makarov, V.S.      204 209 227
Manifold, conformally fiat      134
Manifold, of constant curvature      9
Manifold, protectively fiat      134
Manifold, Riemannian flat      181
Marden, A.      167
Margulis, G.A.      170 226 231 239 240
Maskit, B.      159
Matrix, decomposable      107
Matrix, parabolic      110
Mennicke, J.L.      167
Metric, Riemannian invariant      10
Millson's property      239
Millson, J.J.      239
Milnor, J.      112 123
Minkowski, H.      104 135
Mobius, A.      181
Model, affine      14
Model, affine, standard      14
Model, conformal      41
Model, Euclidean      41
Model, fiat (of a conformal space)      38
Model, Klein      32
Model, matrix      44
Model, Poincare      43
Model, projective      29
Model, projective, Euclidean      31
Model, standard      14
Model, vector      14
Mostow, G.      232
Motion      9
Motion, elliptic      95
Motion, hyperbolic      95
Motion, improper      11
Motion, parabolic      95
Motion, proper      11
Mutually equidistant sets      79
Nielsen's conjecture      197
Nielsen's domain      190
Nielsen, J.      190 197
Nikulin, V.V.      225
Normal coordinates      131
Orbifold      158
Orientation of a hyperplane      23
Ornament      152
Pair of pants      194
Parallel displacement along a line      71 96
Parallelohedron      182
Pencil of lines      51 86
Pencil of lines, elliptic      72 86
Pencil of lines, hyperbolicl      73 86
Pencil of lines, parabolic      74 87
Perpendicular      25
Perpendicular secant for a pair of planes      82
Perron, O.      109
Peterson operator      133
Peterson, K.M.      132
Piatetski-Shapiro, I.I.      228
Plane      21
Plane, Lobachevskij extended      51
Planes      85
Planes, mutually equidistant      79
Planes, orthogonal      24
Planes, parallel (in the sense of Lobachevskij)      82
Planes, perpendicular      79
Planes, polar      24
Poincare's method      164
Poincare's relation      161
Poincare's relation, convex      56
Poincare's relation, fundamental canonical      187
Poincare's relation, proper      56
Poincare's relation, regular      214
Poincare, H.      43 46 120 157 161 196 204
Polyhedron, acute-angled      106
Polyhedron, convex      24
Polyhedron, convex, acute-angled      106
Polyhedron, Coxeter      199
Polyhedron, fundamental      159
Polyhedron, indecomposable      109
Polyhedron, non-degenerate      104
Polyhedron, normal      159
Polyhedron, regular      211
Prasad, G.      231
Projection (orthogonal)      25
Projection, stereographic      37
Quadric, oval      30
Quaternion algebra      218
Quotient space with respect to the action of a discrete group      145
Raghunathan, M.S.      232
Ramification index      184
Ramifiend covering      184
Rank of a scheme      201
Reflection      21
Riemann, B.      19
Rotation about a plane      93
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