Natural operations in differential geometry:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin u.a.
Springer
1993
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 417 - 427, Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | 434 S. |
| ISBN: | 3540562354 0387562354 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV007462319 | ||
| 003 | DE-604 | ||
| 005 | 20131002 | ||
| 007 | t | ||
| 008 | 930517s1993 |||| 00||| engod | ||
| 020 | |a 3540562354 |9 3-540-56235-4 | ||
| 020 | |a 0387562354 |9 0-387-56235-4 | ||
| 035 | |a (OCoLC)320356919 | ||
| 035 | |a (DE-599)BVBBV007462319 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-739 |a DE-12 |a DE-824 |a DE-29T |a DE-355 |a DE-20 |a DE-703 |a DE-19 |a DE-634 |a DE-83 |a DE-11 |a DE-188 | ||
| 080 | |a 517.9 | ||
| 084 | |a SK 370 |0 (DE-625)143234: |2 rvk | ||
| 084 | |a MAT 530f |2 stub | ||
| 084 | |a 53C05 |2 msc | ||
| 100 | 1 | |a Kolář, Ivan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Natural operations in differential geometry |c Ivan Kolář ; Peter W. Michor ; Jan Slovák |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1993 | |
| 300 | |a 434 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Literaturverz. S. 417 - 427, Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 0 | 7 | |a Normaler Operator |0 (DE-588)4304687-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 1 | 1 | |a Normaler Operator |0 (DE-588)4304687-3 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Michor, Peter W. |d 1949- |e Verfasser |0 (DE-588)172276144 |4 aut | |
| 700 | 1 | |a Slovák, Jan |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004843519&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 940 | 1 | |n oe | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-004843519 | ||
Datensatz im Suchindex
| _version_ | 1804121736956870656 |
|---|---|
| adam_text | TABLE OF CONTENTS
PREFACE 1
CHAPTER I. MANIFOLDS AND LIE GROUPS 4
1. Differentiable manifolds 4
2. Submersions and immersions 11
3. Vector fields and flows 16
4. Lie groups 30
5. Lie subgroups and homogeneous spaces 41
CHAPTER II. DIFFERENTIAL FORMS 49
6. Vector bundles 49
7. Differential forms 61
8. Derivations on the algebra of differential forms
and the Frolicher Nijenhuis bracket 67
CHAPTER III. BUNDLES AND CONNECTIONS 76
9. General fiber bundles and connections 76
10. Principal fiber bundles and G bundles 86
11. Principal and induced connections 99
CHAPTER IV. JETS AND NATURAL BUNDLES lie
12. Jets 117
13. Jet groups 128
14. Natural bundles and operators 138
15. Prolongations of principal fiber bundles 149
16. Canonical differential forms 154
17. Connections and the absolute differentiation 158
CHAPTER V. FINITE ORDER THEOREMS 168
18. Bundle functors and natural operators 169
19. Peetre like theorems 176
20. The regularity of bundle functors 185
21. Actions of jet groups 192
22. The order of bundle functors 202
23. The order of natural operators 205
CHAPTER VI. METHODS FOR FINDING NATURAL OPERATORS 212
24. Polynomial GL(T/) equivariant maps 213
25. Natural operators on linear connections, the exterior differential . . 220
26. The tensor evaluation theorem 223
27. Generalized invariant tensors 230
28. The orbit reduction 233
29. The method of differential equations 245
vi Table of Contents
CHAPTER VII. FURTHER APPLICATIONS 249
30. The Frolicher Nijenhuis bracket 250
31. Two problems on general connections 255
32. Jet functors 259
33. Topics from Riemannian geometry 265
34. Multilinear natural operators 280
CHAPTER VIII. PRODUCT PRESERVING FUNCTORS 296
35. Weil algebras and Weil functors 297
36. Product preserving functors 308
37. Examples and applications 318
CHAPTER IX. BUNDLE FUNCTORS ON MANIFOLDS 329
38. The point property 329
39. The flow natural transformation 336
40. Natural transformations 341
41. Star bundle functors 345
CHAPTER X. PROLONGATION OF VECTOR FIELDS AND
CONNECTIONS 350
42. Prolongations of vector fields to Weil bundles 351
43. The case of the second order tangent vectors 357
44. Induced vector fields on jet bundles 360
45. Prolongations of connections to FY —* M 363
46. The cases FY FM and FY Y 369
CHAPTER XL GENERAL THEORY OF LIE DERIVATIVES .... 376
47. The general geometric approach 376
48. Commuting with natural operators 381
49. Lie derivatives of morphisms of fibered manifolds 387
50. The general bracket formula 390
CHAPTER XII. GAUGE NATURAL BUNDLES AND OPERATORS 394
51. Gauge natural bundles 394
52. The Utiyama theorem 399
53. Base extending gauge natural operators 405
54. Induced linear connections on the total space
of vector and principal bundles 409
References 417
List of symbols 428
Author index 429
Index 431
|
| any_adam_object | 1 |
| author | Kolář, Ivan Michor, Peter W. 1949- Slovák, Jan |
| author_GND | (DE-588)172276144 |
| author_facet | Kolář, Ivan Michor, Peter W. 1949- Slovák, Jan |
| author_role | aut aut aut |
| author_sort | Kolář, Ivan |
| author_variant | i k ik p w m pw pwm j s js |
| building | Verbundindex |
| bvnumber | BV007462319 |
| classification_rvk | SK 370 |
| classification_tum | MAT 530f |
| ctrlnum | (OCoLC)320356919 (DE-599)BVBBV007462319 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01826nam a2200457 c 4500</leader><controlfield tag="001">BV007462319</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20131002 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">930517s1993 |||| 00||| engod</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3540562354</subfield><subfield code="9">3-540-56235-4</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0387562354</subfield><subfield code="9">0-387-56235-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)320356919</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV007462319</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-739</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-29T</subfield><subfield code="a">DE-355</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="080" ind1=" " ind2=" "><subfield code="a">517.9</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 370</subfield><subfield code="0">(DE-625)143234:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 530f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">53C05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Kolář, Ivan</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Natural operations in differential geometry</subfield><subfield code="c">Ivan Kolář ; Peter W. Michor ; Jan Slovák</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin u.a.</subfield><subfield code="b">Springer</subfield><subfield code="c">1993</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">434 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Literaturverz. S. 417 - 427, Hier auch später erschienene, unveränderte Nachdrucke</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Normaler Operator</subfield><subfield code="0">(DE-588)4304687-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Differentialgeometrie</subfield><subfield code="0">(DE-588)4012248-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Normaler Operator</subfield><subfield code="0">(DE-588)4304687-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Michor, Peter W.</subfield><subfield code="d">1949-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)172276144</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Slovák, Jan</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004843519&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="940" ind1="1" ind2=" "><subfield code="n">oe</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-004843519</subfield></datafield></record></collection> |
| id | DE-604.BV007462319 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:02:44Z |
| institution | BVB |
| isbn | 3540562354 0387562354 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-004843519 |
| oclc_num | 320356919 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-739 DE-12 DE-824 DE-29T DE-355 DE-BY-UBR DE-20 DE-703 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-91G DE-BY-TUM DE-739 DE-12 DE-824 DE-29T DE-355 DE-BY-UBR DE-20 DE-703 DE-19 DE-BY-UBM DE-634 DE-83 DE-11 DE-188 |
| physical | 434 S. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Springer |
| record_format | marc |
| spelling | Kolář, Ivan Verfasser aut Natural operations in differential geometry Ivan Kolář ; Peter W. Michor ; Jan Slovák Berlin u.a. Springer 1993 434 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 417 - 427, Hier auch später erschienene, unveränderte Nachdrucke Normaler Operator (DE-588)4304687-3 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s DE-604 Normaler Operator (DE-588)4304687-3 s Michor, Peter W. 1949- Verfasser (DE-588)172276144 aut Slovák, Jan Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004843519&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kolář, Ivan Michor, Peter W. 1949- Slovák, Jan Natural operations in differential geometry Normaler Operator (DE-588)4304687-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4304687-3 (DE-588)4012248-7 |
| title | Natural operations in differential geometry |
| title_auth | Natural operations in differential geometry |
| title_exact_search | Natural operations in differential geometry |
| title_full | Natural operations in differential geometry Ivan Kolář ; Peter W. Michor ; Jan Slovák |
| title_fullStr | Natural operations in differential geometry Ivan Kolář ; Peter W. Michor ; Jan Slovák |
| title_full_unstemmed | Natural operations in differential geometry Ivan Kolář ; Peter W. Michor ; Jan Slovák |
| title_short | Natural operations in differential geometry |
| title_sort | natural operations in differential geometry |
| topic | Normaler Operator (DE-588)4304687-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Normaler Operator Differentialgeometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004843519&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT kolarivan naturaloperationsindifferentialgeometry AT michorpeterw naturaloperationsindifferentialgeometry AT slovakjan naturaloperationsindifferentialgeometry |