Theory of multicodimensional n-webs n+1-webs:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht u.a.
Kluwer
1988
|
| Series: | Mathematics and its applications
44 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 440 - 451 |
| Physical Description: | XXI, 466 S. |
| ISBN: | 9027727562 |
Staff View
MARC
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| 245 | 1 | 0 | |a Theory of multicodimensional n-webs n+1-webs |
| 246 | 1 | 3 | |a Theory of multicodimensional n-webs |
| 264 | 1 | |a Dordrecht u.a. |b Kluwer |c 1988 | |
| 300 | |a XXI, 466 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 44 | |
| 500 | |a Literaturverz. S. 440 - 451 | ||
| 650 | 7 | |a Géométrie différentielle |2 ram | |
| 650 | 7 | |a Variedades (geometria diferencial) |2 larpcal | |
| 650 | 4 | |a Webs (Differential geometry) | |
| 830 | 0 | |a Mathematics and its applications |v 44 |w (DE-604)BV008163334 |9 44 | |
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Record in the Search Index
| _version_ | 1804120837262934016 |
|---|---|
| adam_text | Table of Contents
Preface xv
CHAPTER 1
Differential Geometry of Multicodimensional (n + 1) Webs
1.1 Fibrations, Foliations, and f Webs W(d,n,r) of
Codimension r on a Differentiate Manifold Xnr 1
1.1.1 Definitions and Examples 1
1.1.2 Closed Form Equations of a Web W(n + 1, n, r) and
Further Examples 6
1.2 The Structure Equations and Fundamental Tensors of
a Web W(n + l,n,r) 9
1.2.1 Moving Frames Associated with a Web W(n + 1, n, r) 9
1.2.2 The Structure Equations and Fundamental Tensors
of a Web W(n + l,n,r) 11
1.2.3 The Structure Equations and Fundamental Tensors
of a Web W(3,2, r) 16
1.2.4 Special Classes of 3 Webs W(3,2, r) 17
1.3 Invariant Affine Connections Associated with a Web
W(n +l,n,r) 20
1.3.1 The Geometrical Meaning of the Forms wj(£) 20
1.3.2 Affine Connections Associated with an (n + 1) Web 21
1.3.3 The Affine Connections Induced by the Connnection
7n+i on Leaves 23
1.3.4 Affine Connections Associated with 3 Subwebs of an
(n + 1) Web 24
1.4 Webs W(n + 1, n, r) with Vanishing Curvature 31
1.5 Parallelisable(n+1) Webs 34
1.6 (n + 1) Webs with Paratactical 3 Subwebs 38
1.7 (n + 1) Webs with Integrable Diagonal Distributions of
4 Subwebs 39
1.8 (n + 1) Webs with Integrable Diagonal Distributions 42
1.9 Transversally Geodesic (n + 1) Webs 46
1.10 Hexagonal (n + 1) Webs 56
1.11 Isoclinic (n + 1) Webs 58
Notes 65
viii Table of Contents
CHAPTER 2
Almost Grassmann Structures Associated with Webs W(n + l,n,r)
2.1 Almost Grassmann Structures on a Differentiable Manifold 69
2.1.1 The Segre Variety and the Segre Cone 69
2.1.2 Grassmann and Almost Grassmann Structures 72
2.2 Structure Equations and Torsion Tensor of an Almost
Grassmann Manifold 74
2.3 An Almost Grassmann Structure Associated with a Web
W(n + 1, n, r) 81
2.4 Semiintegrable Almost Grassmann Structures and
Transversally Geodesic and Isoclinic (n + 1 ) Webs 84
2.5 Double Webs 87
2.6 Problems of Grassmannisation and Algebraisation and
Their Solution for Webs W(d,n,r),d n + l 90
2.6.1 The Grassmannisation Problem for a
Web W{n + l,n,r) 90
2.6.2 The Grassmannisation Problem for a
Web W{d,n,r), d n + 1 91
2.6.3 The Algebraisation Problem for a Web W(3,2, r) 92
2.6.4 The Algebraisation Problem for a Web W(n + 1, n, r) 94
2.6.5 The Algebraisation Problem for
Webs W(d,n,r),d n + l 95
Notes 101
CHAPTER 3
Local Differentiable n Quasigroups
Associated with a Web W(n + l,n,r)
3.1 Local Differentiable n Quasigroups of a Web W(n + 1, n, r) 102
3.2 Structure of a Web W(n + l,n,r) and Its Coordinate
n Quasigroups in a Neighbourhood of a Point 107
3.3 Computation of the Components of the Torsion and Curvature
Tensors of a Web W(n ¦+¦ l,n,r) in Terms of Its Closed Form
Equations ¦. 110
3.4 The Relations between the Torsion Tensors and Alternators
of Parastrophic Coordinate n Quasigroups 114
3.5 Canonical Expansions of the Equations of a Local
Analytic n Quasigroup 116
3.6 The One Parameter n Subquasigroups of a Local
Differentiable n Quasigroup 125
Table of Contents ix
3.7 Comtrans Algebras 131
3.7.1 Preliminaries 132
3.7.2 Comtrans Structures 133
3.7.3 Masking 135
3.7.4 Lie s Third Fundamental Theorem for Analytic 3 Loops 137
3.7.5 General Case of Analytic n Loops 138
Notes 139
CHAPTER 4
Special Classes of Multicodimensional (n + 1) Webs
4.1 Reducible (n + 1) Webs • 140
4.2 Multiple Reducible and Completely Reducible (n + 1) Webs 147
4.3 Group (n + 1) Webs 151
4.4 (2n + 2) Hedral (n + 1) Webs 158
4.5 Bol (n + i) Webs 162
4.5.1 Definition and Properties of Bol and Moufang
(n + 1) Webs 162
4.5.2 The Bol Closure Conditions 164
4.5.3 A Geometric Characteristic of Bol (n + 1) Webs 173
4.5.4 An Analytic Characteristic of the Bol Closure
Condition (B^l) 180
Notes 188
CHAPTER 5
Realisations of Multicodimensional (n + 1) Webs
5.1 Grassmann (n + 1) Webs 189
5.1.1 Basic Definitions 189
5.1.2 The Structure Equations of Projective Space 191
5.1.3 Specialisation of Moving Frames 193
5.1.4 The Structure Equations and the Fundamental Tensors of
a Grassmann (n + 1) Web 195
5.1.5 Transversally Geodesic and Isoclinic Surfaces of a
Grassmann (n + 1) Web 196
5.1.6 The Hexagonality Tensor of a Grassmann (n + 1) Web and
the 2nd Fundamental Forms of Surfaces U^ 198
5.2 The Grassmannisation Theorem for Multicodimensional
(n + 1) Webs 200
5.3 Reducible Grassmann (n + 1) Webs 203
x Table of Contents
5.4 Algebraic, Bol Algebraic, and Reducible Algebraic (n + 1) Webs 206
5.4.1 General Algebraic (n + 1) Webs 206
5.4.2 Bol Algebraic (n + 1) Webs 207
5.4.3 Reducible Algebraic (n + 1) Webs 209
5.4.4 Multiple Reducible Algebraic (n + 1) Webs 210
5.4.5 Reducible Algebraic Four Webs 213
5.4.6 Completely Reducible Algebraic (n + 1) Webs 214
5.5 Moufang Algebraic (n + 1) Webs 218
5.6 (2n + 2) Hedral Grassmann (n + 1) Webs 222
5.7 The Fundamental Equations of a Diagonal 4 Web Formed by
Four Pencils of (2r) Planes in P3r 226
5.8 The Geometry of Diagonal 4 Webs in P3r 234
Notes 242
CHAPTER 6
Applications of the Theory of (n + 1) Webs
6.1 The Application of the Theory of (n + 1) Webs to the
Theory of Point Correspondences of n + 1 Projective Lines 243
6.1.1 The Fundamental Equations 243
6.1.2 Correspondences among n + 1 Projective Lines and
One Codimensional (n + 1) Webs 248
6.1.3 Parallelisable Correpondences 248
6.1.4 Hexagonal Correspondences 250
6.1.5 The Godeaux Homography 252
6.1.6 Parallelisable Godeaux Homographies 253
6.2 The Application of the Theory of (n + 1) Webs to the Theory
of Point Correspondences of n + 1 Projective Spaces 253
6.2.1 The Fundamental Equations 253
6.2.2 Correspondences among n + 1 Projective Lines and
Multicodimensional (n + 1) Webs 258
6.2.3 Parallelisable Correpondences 260
6.2.4 Godeaux Homographies 260
6.2.5 Parallelisable Godeaux Homographies 262
6.2.6 Paratactical Correspondences 263
6.3 Application of the Theory of (n + 1) Webs to the Theory of
Holomorphic Mappings between Polyhedral Domains 264
6.3.1. Introductory Note 264
6.3.2 Analytical Polyhedral Domains in Cn, n 1 265
6.3.3 Meromorphic Webs in Domains of Cn, n 1 268
6.3.4 Partition Webs Generated by Analytical Polyhedral Domains ... 275
6.3.5 Partition Webs with Parallelisable Foliations 278
Table of Contents xi
6.3.6 Partition Webs with Invariant Functions 286
Notes 295
CHAPTER 7
The Theory of Four Webs W(4,2,r)
7.1 Differential geometry of Four Webs W(4,2, r) 300
7.1.1 Basic Notions and Equations 300
7.1.2 The Geometrical Meaning of the Basis Affinor 302
7.1.3 Transversal Bivectors Associated with a 4 Web 303
7.1.4 Permutability of Transformations [£, r/] 304
7.1.5 Fundamental Equations of a Web VK(4,2, r) 305
7.1.6 The Affine Connections Associated with a Web W(A, 2,r) 308
7.1.7 Conditions of Geodesicity of Some Lines on the Leaves
of a 4 Web in the Canonical Affine Connection 7123 309
7.2 Special Classes of Webs W(4,2,r) 311
7.2.1 Parallelisable Webs W(4,2,r) 311
7.2.2 Webs W(4,2,r) with Special 3 Subwebs 312
7.2.3 Group Webs W(4,2,r) 317
7.2.4 Parallelisable Webs W(4,2, r) (Continuation) 318
7.2.5 Webs W(4,2, r) with a Group 3 Subweb 319
7.3 The Canonical Expansions of the Equations of a Pair of Orthogonal
Quasigroups Associated with a Web W(4,2, r) 325
7.3.1 A Pair of Orthogonal Quasigroups Associated with
a Web W(4,2,r) 325
7.3.2 The Canonical Expansions of the Equations of the
Quasigroups A and B 326
7.4 Webs W(4,2, r) Satisfying the Desargues and Triangle Closure
Conditions 330
7.4.1 Webs W(A, 2, r) Satisfying the Desargues Closure Condition Dj . 330
7.4.2 Group Webs and Webs W(4,2, r) Satisfying Two Desargues
Closure Conditions, D and D^ 334
7.4.3 Webs W(4,2, r) Satisfying the Desargues Closure Condition Du 337
7.4.4 Webs W(4,2, r) Satisfying the Triangle Closure Conditions 339
7.4.5 Properties of Orthogonal Quasigroups Associated with Webs
W(4,2, r) Satisfying the Desargues and Triangle Closure
Conditions 342
7.5 A Classification of Group Webs W(4,2,3) 344
7.6 Grassmann Webs GW(4,2,r) 350
7.6.1 Basic Notions 350
7.6.2 Specialisation of Moving Frames 351
7.6.3 The Structure Equations, the Fundamental Tensors, and the
Basis Affinor of a Grassmann Web GW(A, 2, r) 353
xii Table of Contents
7.6.4 The Connection Forms and the Fundamental Tensors of
3 Subwebs of a Grassmann Web GW(4,2, r) 355
7.7 Grassmann Webs GW(i, 2, r) with Algebraic 3 Subwebs 356
7.8 Algebraic Webs AW(4,2, r) 362
Notes 373
CHAPTER 8
Rank Problems for Webs W(d, 2, r)
8.1 Almost Grassmannisable and Almost Algebraisable Webs W(d,2,r) .. 374
8.1.1 Basic Notions and Equations for a Web W(d,2,r),d 3 374
8.1.2 Almost Grassmannisable Webs AGW(d, 2, r), d 3 376
8.1.3 Isoclinic Almost Grassmannisable Webs AGW(d, 2, r) 382
8.1.4 Almost Algebraisable Webs AAW(d,2,r) 385
8.1.5 Non Isoclinic Almost Grassmannisable Webs AGW{4,2,2) 388
8.1.6 Examples of Non Extendable Non Isoclinic Webs W{3,2,2) 390
8.2 1 Rank Problems for Almost Grassmannisable Webs AGW(d,2,r) .... 393
8.2.1 Basic Equations for a Web W(d, 2, r) of Non Zero 1 Rank 393
8.2.2 The Upper Bound for the 1 Rank of an Almost
Grassmannisable Web AGW(d, 2, r),r 1 395
8.2.3 Description of the Webs AGW(d,2,r),d 4,r 1, of
Maximum 1 Rank 402
8.2.4 Explicit Expressions of the Functions tp^ and Description
of Their Level Sets 404
8.3 r Rank Problems for Webs W(d,2,r) 406
8.3.1 The r Rank of Webs W(d,n,r) 406
8.3.2 Almost Grassmannisable Webs AGW(d, 2,2) of Maximum
2 Rank 410
8.3.3 Webs W(d,2,2),d 4, of Maximum 2 Rank 413
8.3.4 Four Webs W(4,2,2) of Maximum 2 Rank 414
8.4 Examples of Webs W(4,2,2) of Maximum 2 Rank 417
8.4.1 The Isoclinic Case 417
8.4.2 The Non Isoclinic Case 428
8.5 The Geometry of The Exceptional Webs W(4,2,2) of Maximum
2 Rank 432
8.5.1 Double Fibrations and Webs 432
8.5.2 Interior Products Associated with an Exceptional
Four Web 433
Table of Contents xiii
8.5.3 Exterior 3 Forms Associated with an Exceptional
Four Web 435
8.5.4 Infinitesimal Automorphisms of Exterior Cubic Forms
Associated with an Exceptional Four Web 436
8.5.5 Infinitesimal Conformal Transformations of Exterior
Cubic Forms Associated with an Exceptional Four Web 438
Notes 438
Bibliography 440
Symbols Frequently Used 452
Index 455
|
| any_adam_object | 1 |
| author | Golʹdberg, Vladislav V. 1936- |
| author_GND | (DE-588)128639644 |
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| dewey-ones | 516 - Geometry |
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| dewey-sort | 3516.3 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV006566853 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:48:26Z |
| institution | BVB |
| isbn | 9027727562 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004188924 |
| oclc_num | 17952144 |
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| owner | DE-739 |
| owner_facet | DE-739 |
| physical | XXI, 466 S. |
| publishDate | 1988 |
| publishDateSearch | 1988 |
| publishDateSort | 1988 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Golʹdberg, Vladislav V. 1936- Verfasser (DE-588)128639644 aut Theory of multicodimensional n-webs n+1-webs Theory of multicodimensional n-webs Dordrecht u.a. Kluwer 1988 XXI, 466 S. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 44 Literaturverz. S. 440 - 451 Géométrie différentielle ram Variedades (geometria diferencial) larpcal Webs (Differential geometry) Mathematics and its applications 44 (DE-604)BV008163334 44 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004188924&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Golʹdberg, Vladislav V. 1936- Theory of multicodimensional n-webs n+1-webs Mathematics and its applications Géométrie différentielle ram Variedades (geometria diferencial) larpcal Webs (Differential geometry) |
| title | Theory of multicodimensional n-webs n+1-webs |
| title_alt | Theory of multicodimensional n-webs |
| title_auth | Theory of multicodimensional n-webs n+1-webs |
| title_exact_search | Theory of multicodimensional n-webs n+1-webs |
| title_full | Theory of multicodimensional n-webs n+1-webs |
| title_fullStr | Theory of multicodimensional n-webs n+1-webs |
| title_full_unstemmed | Theory of multicodimensional n-webs n+1-webs |
| title_short | Theory of multicodimensional n-webs n+1-webs |
| title_sort | theory of multicodimensional n webs n 1 webs |
| topic | Géométrie différentielle ram Variedades (geometria diferencial) larpcal Webs (Differential geometry) |
| topic_facet | Géométrie différentielle Variedades (geometria diferencial) Webs (Differential geometry) |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004188924&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT golʹdbergvladislavv theoryofmulticodimensionalnwebsn1webs AT golʹdbergvladislavv theoryofmulticodimensionalnwebs |