Theory of holors: a generalization of tensors
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Pr.
1986
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 392 S. Ill. |
| ISBN: | 0521245850 |
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MARC
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| 245 | 1 | 0 | |a Theory of holors |b a generalization of tensors |c Parry Moon ; Domina Eberle Spencer |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge u.a. |b Cambridge Univ. Pr. |c 1986 | |
| 300 | |a XIX, 392 S. |b Ill. | ||
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Record in the Search Index
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| adam_text | Contents
Preface page xiii
Nomenclature xv
0 Historical introduction 1
0.01 Quaternions 1
0.02 Linear associative algebras 2
0.03 Matrices 3
0.04 Grassmann 3
0.05 Vector analysis 4
0.06 Invariance 4
0.07 Tensors 5
0.08 Holor notation 6
0.09 Derivatives 7
0.10 Outline of the book 8
I Holors
1 Index notation 11
1.01 Variety of holors 12
1.02 Notation 14
1.03 Conventions 15
1.04 The transpose 18
1.05 Symmetry and antisymmetry 19
1.06 Diagonal holors 21
1.07 Generalized Kronecker deltas 22
1.08 Summary 26
Problems 27
vii
viii Contents
2 Holor algebra 30
2.01 Equality of holors 30
2.02 Addition of holors 32
2.03 The uncontracted product 36
2.04 The contracted product 40
2.05 Matrices 43
2.06 Index balance 45
2.07 Unit holors 47
2.08 The inverse 49
2.09 General conditions for an inverse 55
2.10 Null products 57
2.11 Cancellation rule for products 59
2.12 Summary 59
Problems 61
3 Gamma products 65
3.01 Change of index positions 66
3.02 Change of valence 67
3.03 Symmetric and antisymmetric matrices 69
3.04 Products of univalent holors 72
3.05 Nilvalent products 75
3.06 Univalent products 76
3.07 Alternating currents 78
3.08 Bivalent products 80
3.09 Other products 81
3.10 Summary 83
Problems 83
II Transformations
4 Tensors 89
4.01 Linear transformations 89
4.02 Invariants 91
4.03 Groups 94
4.04 General transformations 95
4.05 Geometric objects 97
4.06 Univalent tensors 99
4.07 Other tensors 100
4.08 Tensor algebra 105
4.09 Tensor equations 108
4.10 Tensor character 111
Contents ix
4.11 Tensors with fixed merates 114
4.12 Summary 117
Problems 119
5 Akinetors 126
5.01 Definitions 128
5.02 Algebra 129
5.03 The akinetor as generalization of the tensor 131
5.04 Combinations 134
5.05 Derivatives 136
5.06 Combinations of derivatives 139
5.07 Pseudodivergence 141
5.08 Pseudocurl 143
5.09 Other akinetors 145
5.10 Summary 148
Problems 152
6 Geometric spaces 156
6.01 Arithmetic space 157
6.02 Invariants 158
6.03 Transformations 160
6.04 Afnne space 162
6.05 Parting 165
6.06 Ratios of areas and of volumes 167
6.07 Second degree surfaces 168
6.08 Axonometric space 170
6.09 Homogeneous coordinates 178
6.10 The projective transformation 180
6.11 Projective space 181
6.12 Perspective space 189
6.13 Inversions 193
6.14 Homogeneous coordinates in afnne space 195
6.15 Bivalent tensors in afnne space 197
6.16 Summary 203
Problems 203
III Holor calculus
7 The linear connection 211
7.01 The linear connection 213
7.02 The covariant derivatives of a contravariant vector 215
7.03 The covariant derivatives of a covariant vector 218
x Contents
7.04 The covariant derivatives of bivalent tensors 219
7.05 Covariant derivatives of tensors of valence m 222
7.06 Contracted covariant derivatives 229
7.07 Derivatives with respect to a scalar parameter 232
7.08 The covariant derivatives of akinetors 234
7.09 Summary 238
Problems 239
8 The Riemann Christoffel tensors 242
8.01 Second covariant derivatives of scalars 242
8.02 Second covariant derivatives of contravariant vectors 243
8.03 Second covariant derivatives of covariant vectors 246
8.04 Second covariant derivatives of tensors 246
8.05 Second covariant derivatives of nilvalent akinetors 248
8.06 Second covariant derivatives of akinetors 249
8.07 Integrability of scalar fields 251
8.08 Integrability of contravariant vector fields 253
8.09 Integrability of covariant vector fields 256
8.10 Integrability of tensor fields 258
8.11 Integrability of nilvalent akinetor fields 260
8.12 Integrability of akinetor fields 262
8.13 Properties of the Riemann Christoffel tensors 264
8.14 The Bianchi identities 266
8.15 Summary 268
Problems 270
IV Space structure
9 Non Riemannian spaces 275
9.01 The absolute differential 275
9.02 Homeomorphic displacements 279
9.03 The infinitesimal pentagon 282
9.04 Linearly connected spaces 285
9.05 Equations of paths 288
9.06 Parameter transformation 291
9.07 Weyl space 292
9.08 Projectively connected space 294
9.09 Projective invariants 296
9.10 Summary 297
Problems 297
Contents xi
10 Riemannian space 300
10.01 The metric tensor 301
10.02 Modifications 304
10.03 The linear connection 308
10.04 Geodesies 314
10.05 Curvature 318
10.06 Homeomorphic transport of a vector 320
10.07 Volume and area 324
10.08 Scalar and vector products 326
10.09 Gradient, divergence, and curl 331
10.10 Theorems of Gauss and Stokes 336
10.11 The scalar and vector Laplacians 337
10.12 The contracted covariant derivative of a bivalent tensor 340
10.13 Summary 341
Problems 342
11 Euclidean space 346
11.01 Definition of Euclidean space 347
11.02 Metric coefficients 348
11.03 The linear connection 351
11.04 Merates and components 351
11.05 Euclidean /7 space 353
11.06 Skew coordinates 354
11.07 Euclidean 3 space 358
11.08 Index notation versus vector notation 360
11.09 Sliding vectors 361
11.10 Sums of sliding vectors 365
11.11 Summary 369
Problems 370
References 376
Index 387
|
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| edition | 1. publ. |
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| indexdate | 2024-07-09T15:15:51Z |
| institution | BVB |
| isbn | 0521245850 |
| language | English |
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| physical | XIX, 392 S. Ill. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | Cambridge Univ. Pr. |
| record_format | marc |
| spelling | Moon, Parry Verfasser aut Theory of holors a generalization of tensors Parry Moon ; Domina Eberle Spencer 1. publ. Cambridge u.a. Cambridge Univ. Pr. 1986 XIX, 392 S. Ill. txt rdacontent n rdamedia nc rdacarrier Calcul tensoriel Calcul tensoriel ram Calculus of tensors Tensoranalysis (DE-588)4204323-2 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 gnd rswk-swf Tensorrechnung (DE-588)4192487-3 s DE-604 Tensoranalysis (DE-588)4204323-2 s Spencer, Domina Eberle 1920- Verfasser (DE-588)115563059 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000351423&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Moon, Parry Spencer, Domina Eberle 1920- Theory of holors a generalization of tensors Calcul tensoriel Calcul tensoriel ram Calculus of tensors Tensoranalysis (DE-588)4204323-2 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| subject_GND | (DE-588)4204323-2 (DE-588)4192487-3 |
| title | Theory of holors a generalization of tensors |
| title_auth | Theory of holors a generalization of tensors |
| title_exact_search | Theory of holors a generalization of tensors |
| title_full | Theory of holors a generalization of tensors Parry Moon ; Domina Eberle Spencer |
| title_fullStr | Theory of holors a generalization of tensors Parry Moon ; Domina Eberle Spencer |
| title_full_unstemmed | Theory of holors a generalization of tensors Parry Moon ; Domina Eberle Spencer |
| title_short | Theory of holors |
| title_sort | theory of holors a generalization of tensors |
| title_sub | a generalization of tensors |
| topic | Calcul tensoriel Calcul tensoriel ram Calculus of tensors Tensoranalysis (DE-588)4204323-2 gnd Tensorrechnung (DE-588)4192487-3 gnd |
| topic_facet | Calcul tensoriel Calculus of tensors Tensoranalysis Tensorrechnung |
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