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
Akivis M., Goldberg V. — Differential Geometry of Varieties with Degenerate Gauss Maps
Akivis M., Goldberg V. — Differential Geometry of Varieties with Degenerate Gauss Maps



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Differential Geometry of Varieties with Degenerate Gauss Maps

Авторы: Akivis M., Goldberg V.

Аннотация:

In this book the authors study the differential geometry of varieties with degenerate Gauss maps. They use the main methods of differential geometry, namely, the methods of moving frames and exterior differential forms as well as tensor methods. By means of these methods, the authors discover the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.The authors introduce the above mentioned methods and apply them to a series of concrete problems arising in the theory of varieties with degenerate Gauss maps. What makes this book unique is the authors' use of a systematic application of methods of projective differential geometry along with methods of the classical algebraic geometry for studying varieties with degenerate Gauss maps. This book is intended for researchers and graduate students interested in projective differential geometry and algebraic geometry and their applications. It can be used as a text for advanced undergraduate and graduate students. Both authors have published over 100 papers each. Each has written a number of books, including Conformal Differential Geometry and Its Generalizations (Wiley 1996), Projective Differential Geometry of Submanifolds (North-Holland 1993), and Introductory Linear Algebra (Prentice-Hall 1972), which were written by them jointly.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 234

Добавлена в каталог: 10.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$\lambda$-equation      137 151
$\mathbb{A}$-smooth line      214
$\mathbb{P}^m$-equivalent points      24
0-pair      194
2-plane at infinity      120
Abe      172 221
Absolute      126—128 177 181 183
Absolute invariant      5
Absolute invariant of curve      38
Absolute of $\mathbb{H}^n$      127
Absolute of $\mathbb{S}^n$      126
Adjacent points      209
Admissible transformation(s)      18 52 54
Affine analogue of Hartman — Nirenberg cylinder theorem      150 172
Affine connection      18 19 47
Affine frame      25 26
Affine parameter      76
Affine space      25 118 122 133 150 154 164 196 199 203 218
Affine space, structure equations of      26 203
Affine transformation(s)      18 25
Affinely complete hypersurface      154
Akivis      xiv—xviii xx 15 46 86—89 101 134 149 154 164 169 176 178 179 184 189 194 199 202 203 219 221—223
Algebra of Cayley's octonions      90
Algebra of complex numbers      90 207 219
Algebra of double numbers      207 219
Algebra of dual numbers      207 219
Algebra of quaternions      90
Algebra of split numbers      207
Algebraic cone      198
Algebraic equation      69
Algebraic fourth-degree surface      68
Algebraic geometry      87 88
Algebraic hypercone      101
Algebraic hypersurface      100 101 197
Algebraic hypersurface with degenerate Gauss map      90
Algebraic variety      42
Allendoerfer      xiv 87 223
Almost everywhere differentiable function      50
Almost everywhere differentiable mapping      49
Almost everywhere differentiable variety      49 51
Alternation      42
Analytic function      7
Analytic manifold      5
Anticommutativity      9
Antiinvolutive automorphism      90
Arnold      xv 103 223
Asymptotic cone(s) of Grassmannian      60
Asymptotic cone(s) of hypersurface      61
Asymptotic cone(s) of variety      58
Asymptotic curve      58 164
Asymptotic direction      86 154 156
Asymptotic tangent      156
Autopolar simplex      27
Axial point      61 62
Band      164 173
Base form(s)      52
Basic equations of variety      52
Basic equations of variety with degenerate Gauss map      94 151
Basis      1
Basis form(s) of $\mathbb{A}$-smooth line      214
Basis form(s) of curve      28
Basis form(s) of focal line      158
Basis form(s) of Gauss image      93
Basis form(s) of Grassmannian      42 53 63
Basis form(s) of hypersurface      182
Basis form(s) of manifold      16 17
Basis form(s) of Monge — Ampere foliation      92
Basis form(s) of parametric manifold      185
Basis form(s) of torse      138 115
Basis form(s) of variety      52
Basis form(s) of variety with degenerate Gauss map      92
Basis hyperplane      145
Basis natural      15
Basis natural of cotangent space      22
Basis natural of dual space      6
Basis natural of fibration      98
Basis natural of projectivization      24
Basis natural of tangent space      22
Basis natural of vector space      1 20
Basis points of plane      209
Basis points of second normal subspace      57
Basis points of subspace      41
Basis vectors      26
Bejancu      218 227
Beltrametti      89 223
Bianchi      xiv 87 223
Bijective mapping      8
Bilinear form      10
Bisecant      44 105
Bisecant variety      44 46
Blaschke      xix 58 164 223 224
Block diagonal form      165
Boecher      137 224
Borisenko      88 134 172 224
Bourbaki      208 219 224
Brauner      xiv 87 224
Bruce      xiv 224
Bryant      xx 15 46 216 225
Bundle cotangent      6
Bundle of first-order frames      52
Bundle of hyperplanes      101 136 139—142
Bundle of second fundamental forms      55
Canal hypersurface      186 189 190
Cartan      xiv xx 11 46 47 86 87 89 206 225
Cartan lemma      10
Cartan number      15 131 132 156 158 162 217
Cartan test      13 15 130—132 157 158 162 216 217
Cartesian coordinates      116 119 123
Cauchy horizon      176
Caustic      103 186 191
Cayley      66—69 225
Cayley's parameterization      68
Center(s) of bundle of hyperplanes      136 140—142
Center(s) of pencil of cubics      40
Center(s) of pencil of straight lines      164
Center(s) projectivization      24 52 53
Chakmazyan      203 218 222 225 226
Chandrasekhar      177 218 226
Character(s)      14 15 156
Characteristic equation of matrix with respect to matrix      186
Characteristic subspace      102 137 138
Chern      xx 15 46 47 63 88 133 134 216 225 226
Chern — Lashof — Hartman — Nirenberg lemma      133
Class of differentiable manifold      5
Class of differentiable mapping      7
Classification of three-dimensional varieties      104—105 134 164 173
Closed contour      203
Closed linear form      5
Closed p-form      12
Closure      71
Cobasis      6 51
Coframe      18 23
Collinear vectors      19
Compact hypersurface      88
Complete matrix algebra      207
Complete noncylindrical hypersurface      163
Complete parabolic variety      126 127 134
Complete regular variety      118
Completely integrable system      13 16 92 95 205
Completely reducible system of matrices      165
Completely reducible variety      165 168
Complex conjugate 2-planes      112
Complex conjugate hypercones      113
Complex conjugate points      113 115
Complex manifold      6
Complex numbers, field of      1
Complex projective geometry      88
Component      165 ff.
Conditions for a point to be fixed      31
Cone(s)      64—66 74 102—105 108 127 135 154 156 164 169 172
Conformal space      176 177 184 186 218
Congruence      103 196 199
Conic(s)      35 45 46 79 80 103 107—109 113 120 123
Conic(s) conjugate net      105
Conic(s) curve      188
Conic(s) singular point      188 190 191
Conisecant plane      46
Conjugate net      105 188
Connected hypersurface      149
Connected variety      150
Connection form(s)      19
Connection form(s) of affine connection      201
Connection form(s) of de Sitter space      180
Connection form(s) of normal connection      202
Constant zero curvature      149
Convex hyperquadric      126
Coordinates of tangent vector      6
Correlation      23 80 81
Correlative transformation      80
Cotangent bundle      6
Cotangent space      6 22
Cotangent space, basis of      22
Covariant differential      201 202
Covector      3
Covector field      9
Cubic hypersurface      77 85 88 119
Cubic symmetroid      46 77 103 144 145
Cubic symmetroid, tangent hyperplane to      80
Curvature of line      217
Curvature, form of affine connection      201
Curvature, form of de Sitter space      180—181
Curvature, form of normal connection      202
Curvature, tensor of affine connection      202 204 206
Curvature, tensor of de Sitter space      181
Curvature, tensor,      19
Curve in a projective plane      28 ff.
Curve with constant projective curvature      40
Curve with zero projective curvature      40
Curve, basis form of      28
Cyclic generator      189
Cyclic group      21
Cyclic variable      124
Cylinder      64 127 128 149 150 154 163
Cylinder theorem      149—150 172
Cylindrical variety      88
Darboux      47 226
Darboux, hyperquadric      177 192 194
Darboux, mapping      177 184
De Sitter space      176 ff. 218
Degenerate, focus variety      102
Degenerate, Gauss map      64
Degenerate, hyperquadric      145
Degenerate, Riemannian metric      176
Degenerate, second fundamental form      97 99
Degenerate, symmmetric affinor      187
Delanoe      92 133 226
Derivational formulas      2
Determinant submanifold      44 47 145 195
Developable surface      64 87 133 172
Dieudonne      5 19 46 47 97 226 227
Differentiable coordinates      50
Differentiable covector field      9
Differentiable function      2 5 7 9
Differentiable manifold      5 21 46 49 51
Differentiable mapping      7
Differentiable mapping, class of      7
Differential 1-form      2
Differential equations of 1-form      9
Differential equations of absolute invariant      5
Differential equations of covector      3—4
Differential equations of p-form      9
Differential equations of relative invariant      5
Differential equations of relative tensor      4
Differential equations of subspace      12
Differential equations of tensor      4
Differential equations of tensor field      6
Differential equations of vector      3
Differential of function      9
Differential of Gauss map      185
Differential operator $\delta$      6—7
Differential prolongation      15
Differentiation, exterior      11
Differentiation, exterior, of product      11
Differentiation, relative to secondary parameters      6—7
Dimension of bundle of second fundamental forms      55
Dimension of bundle of tangent hyperplanes      71
Dimension, differentiable manifold      5
Dimension, dual variety      71 72 96
Dimension, frame bundle      6
Dimension, free module      9
Dimension, Grassmannian      59
Dimension, leaf of Monge — Ampere foliation      72
Dimension, osculating subspace to Grassmannian      60
Dimension, projectivization      24
Dimension, second normal subspace      57
Dimension, second osculating subspace      101
Dimension, Segre cone      44
Dimension, Segre variety      44 75
Dimension, tangent bundle      6
Dimension, tangent subspace to Grassmannian      60
Direct product      44
Director variety of cone      65
Director variety of cylinder      150
Discriminant of polynomial      68
distribution      13 202 205
Distribution focus      117 154 157 164 213
Distribution hyperplane      145
Distribution point of cubic      35—37
Distribution straight line      46
Distribution, invariant      19
do Carmo      47 226
Double conic      46
Dual basis      6
Dual coframe      23 97
Dual curve      67
Dual defect of dually nondegenerate variety      90
Dual defect of Segre variety      71 76
Dual defect of tangentially nondegenerate variety      71
Dual defect of variety with degenerate Gauss map      72 89
Dual element of      6
Dual map      70 72 73
Dual space      22 70 82 101
Dual tangent space      6 72
Dual theorem      23
Dual variety      71 96 101
Dual variety of cone      74
Dual variety of hypersurface      74
Dual variety of smooth curve      73
Dual variety of tangentially nondegenerate variety      71
Dual variety of variety with degenerate Gauss map      71 72
Dual vector space      3
Duality principle      22 70 89
Dually degenerate variety      71 72 89 97 101
Dually nondegenerate variety      72 81 90 99 101
Dubrovin      96 227
Duggal      218 227
Edge of regression      102 127 128 188
Eigenvalue      139 140 142 150—152 170
Ein      89 227
Einstein space      181
Einstein summation convention      1
Eisenbud      47 227
Element of dual tangent space      6
Element of tangent bundle      6
Elliptic congruence      211 213
Elliptic pencil of hyperspheres      178
Elliptic space      126—128
Elliptic transformation(s)      27
Embedding      44
Embedding theorem      169 ff.
1 2 3 4 5
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2020
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте