Introduction to global variational geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
[Paris]
Atlantis Press
2015
|
| Series: | Atlantis studies in varionational geometry
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 354 S. |
| ISBN: | 9789462390720 |
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MARC
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| 245 | 1 | 0 | |a Introduction to global variational geometry |c Demeter Krupka |
| 264 | 1 | |a [Paris] |b Atlantis Press |c 2015 | |
| 300 | |a XVII, 354 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-027525729 | ||
Record in the Search Index
| _version_ | 1804152538066321408 |
|---|---|
| adam_text | Contents
1
Jet Prolongations
of Fibered Manifolds
.................... 1
1.1
The Rank Theorem
............................... 1
1.2
Fibered Manifolds
................................ 6
1.3
The Contact of Differentiable Mappings
................ 10
1.4
Jet Prolongations of Fibered Manifolds
................. 13
1.5
The Horizontalization
............................. 17
1.6
Jet Prolongations of Automorphisms of Fibered Manifolds.
... 20
1.7
Jet Prolongations of Vector Fields
..................... 23
References
.......................................... 33
2
Differential Forms on Jet Prolongations of Fibered Manifolds.
... 35
2.1
The Contact Ideal
................................ 35
2.2
The Trace Decomposition
.......................... 43
2.3
The Horizontalization
............................. 53
2.4
The Canonical Decomposition
....................... 58
2.5
Contact Components and Geometric Operations
........... 67
2.6
Strongly Contact Forms
............................ 68
2.7
Fibered Homotopy Operators on Jet Prolongations
of Fibered Manifolds
.............................. 74
References
.......................................... 84
3
Formal Divergence Equations
........................... 85
3.1
Formal Divergence Equations
........................ 85
3.2
Integrabiliry of Formal Divergence Equations
............. 89
3.3
Projectable Extensions of Differential Forms
............. 93
Reference
.......................................... 101
xvi
Contents
4
Variational Structures
................................. 103
4.1
Variational Structures on Fibered Manifolds
.............. 104
4.2
Variational Derivatives
............................ 108
4.3
Lepage Forms
.................................. 112
4.4
Euler-Lagrange Forms
............................. 123
4.5
Lepage Equivalents and the Euler-Lagrange Mapping
....... 124
4.6
The First Variation Formula
......................... 129
4.7
Extremals
...................................... 130
4.8
Trivial Lagrangians
............................... 133
4.9
Source Forms and the Vainberg-Tonti Lagrangians
......... 135
4.10
The Inverse Problem of the Calculus of Variations
......... 146
4.11
Local Variationality of Second-Order Source Forms
........ 157
References
.......................................... 166
5
Invariant Variational Structures
......................... 169
5.1
Invariant Differential Forms
......................... 170
5.2
Invariant Lagrangians and Conservation Equations
......... 172
5.3
Invariant Euler-Lagrange Forms
...................... 177
5.4
Symmetries of Extremals and Jacobi Vector Fields
......... 178
References
.......................................... 185
6
Examples: Natural
Lagrange
Structures
................... 187
6.1
The Hubert Variational Functional
.................... 188
6.2
Natural
Lagrange
Structures
......................... 194
6.3
Connections
.................................... 197
References
.......................................... 200
7
Elementary Sheaf Theory
.............................. 201
7.1
Sheaf Spaces
................................... 201
7.2
Abelian Sheaf Spaces
............................. 207
7.3
Sections of Abelian Sheaf Spaces
..................... 211
7.4
Abelian Presheaves
............................... 213
7.5
Sheaf Spaces Associated with Abelian Presheaves
.......... 217
7.6
Sheaves Associated with Abelian Presheaves
............. 221
7.7
Sequences of Abelian Groups, Complexes
............... 226
7.8
Exact Sequences of Abelian Sheaves
................... 238
7.9
Cohomology Groups of a Sheaf
...................... 242
7.10
Sheaves over Paracompact Hausdorff Spaces
............. 250
References
....................... 261
Contents xvii
8 Variational
Sequences.................................
263
8.1
The Contact Sequence
............................. 264
8.2
The Variational Sequence
.......................... 272
8.3
Variational Projectors
............................. 273
8.4
The Euler-Lagrange Morphisms
...................... 288
8.5
Variationally Trivial Lagrangians
..................... 296
8.6
Global Inverse Problem of the Calculus of Variations
....... 298
References
.......................................... 300
Appendix: Analysis on Euclidean Spaces and Smooth Manifolds
..... 303
Bibliography
........................................... 341
Index
................................................ 347
|
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| id | DE-604.BV042084729 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:12:18Z |
| institution | BVB |
| isbn | 9789462390720 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027525729 |
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| owner | DE-355 DE-BY-UBR DE-384 |
| owner_facet | DE-355 DE-BY-UBR DE-384 |
| physical | XVII, 354 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Atlantis Press |
| record_format | marc |
| series | Atlantis studies in varionational geometry |
| series2 | Atlantis studies in varionational geometry |
| spelling | Krupka, Demeter 1942- Verfasser (DE-588)141633042 aut Introduction to global variational geometry Demeter Krupka [Paris] Atlantis Press 2015 XVII, 354 S. txt rdacontent n rdamedia nc rdacarrier Atlantis studies in varionational geometry 1 Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s DE-604 Erscheint auch als Online-Ausgabe 978-94-6239-073-7 Atlantis studies in varionational geometry 1 (DE-604)BV042324060 1 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027525729&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Krupka, Demeter 1942- Introduction to global variational geometry Atlantis studies in varionational geometry Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4012248-7 |
| title | Introduction to global variational geometry |
| title_auth | Introduction to global variational geometry |
| title_exact_search | Introduction to global variational geometry |
| title_full | Introduction to global variational geometry Demeter Krupka |
| title_fullStr | Introduction to global variational geometry Demeter Krupka |
| title_full_unstemmed | Introduction to global variational geometry Demeter Krupka |
| title_short | Introduction to global variational geometry |
| title_sort | introduction to global variational geometry |
| topic | Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027525729&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV042324060 |
| work_keys_str_mv | AT krupkademeter introductiontoglobalvariationalgeometry |