Transformation Groups in Differential Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1995
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
2. Folge ; 70 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric structures. All geometric structures are not created equal; some are creations of gods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geometric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lectures I gave in Tokyo and Berkeley in 1965 |
| Beschreibung: | 1 Online-Ressource (VIII, 182p) |
| ISBN: | 9783642619816 9783540586593 |
| ISSN: | 0071-1136 |
| DOI: | 10.1007/978-3-642-61981-6 |
Internformat
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| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
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| author | Kobayashi, Shoshichi |
| author_facet | Kobayashi, Shoshichi |
| author_role | aut |
| author_sort | Kobayashi, Shoshichi |
| author_variant | s k sk |
| building | Verbundindex |
| bvnumber | BV042422836 |
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| ctrlnum | (OCoLC)1165442282 (DE-599)BVBBV042422836 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-61981-6 |
| format | Electronic eBook |
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| id | DE-604.BV042422836 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642619816 9783540586593 |
| issn | 0071-1136 |
| language | English |
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| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 1995 |
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| publisher | Springer Berlin Heidelberg |
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| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Classics in Mathematics Ergebnisse der Mathematik und ihrer Grenzgebiete : 2. Folge |
| spelling | Kobayashi, Shoshichi Verfasser aut Transformation Groups in Differential Geometry by Shoshichi Kobayashi Berlin, Heidelberg Springer Berlin Heidelberg 1995 1 Online-Ressource (VIII, 182p) txt rdacontent c rdamedia cr rdacarrier Classics in Mathematics 0071-1136 Ergebnisse der Mathematik und ihrer Grenzgebiete : 2. Folge 70 Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. The object of this book is to give a biased account of automorphism groups of differential geometric structures. All geometric structures are not created equal; some are creations of gods while others are products of lesser human minds. Amongst the former, Riemannian and complex structures stand out for their beauty and wealth. A major portion of this book is therefore devoted to these two structures. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure. Basic theorems in this regard are presented in §§ 3, 4 and 5. The concept of G-structure or that of pseudo-group structure enables us to treat most of the interesting geometric structures in a unified manner. In § 8, we sketch the relationship between the two concepts. Chapter I is so arranged that the reader who is primarily interested in Riemannian, complex, conformal and projective structures can skip §§ 5, 6, 7 and 8. This chapter is partly based on lectures I gave in Tokyo and Berkeley in 1965 Mathematics Group theory Global differential geometry Differential Geometry Group Theory and Generalizations Mathematik Systemtransformation (DE-588)4060633-8 gnd rswk-swf Transformationsgruppe (DE-588)4127386-2 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Transformationsgruppe (DE-588)4127386-2 s 1\p DE-604 Systemtransformation (DE-588)4060633-8 s 2\p DE-604 Ergebnisse der Mathematik und ihrer Grenzgebiete 2. Folge ; 70 (DE-604)BV020546983 70 https://doi.org/10.1007/978-3-642-61981-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kobayashi, Shoshichi Transformation Groups in Differential Geometry Ergebnisse der Mathematik und ihrer Grenzgebiete Mathematics Group theory Global differential geometry Differential Geometry Group Theory and Generalizations Mathematik Systemtransformation (DE-588)4060633-8 gnd Transformationsgruppe (DE-588)4127386-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| subject_GND | (DE-588)4060633-8 (DE-588)4127386-2 (DE-588)4012248-7 |
| title | Transformation Groups in Differential Geometry |
| title_auth | Transformation Groups in Differential Geometry |
| title_exact_search | Transformation Groups in Differential Geometry |
| title_full | Transformation Groups in Differential Geometry by Shoshichi Kobayashi |
| title_fullStr | Transformation Groups in Differential Geometry by Shoshichi Kobayashi |
| title_full_unstemmed | Transformation Groups in Differential Geometry by Shoshichi Kobayashi |
| title_short | Transformation Groups in Differential Geometry |
| title_sort | transformation groups in differential geometry |
| topic | Mathematics Group theory Global differential geometry Differential Geometry Group Theory and Generalizations Mathematik Systemtransformation (DE-588)4060633-8 gnd Transformationsgruppe (DE-588)4127386-2 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Mathematics Group theory Global differential geometry Differential Geometry Group Theory and Generalizations Mathematik Systemtransformation Transformationsgruppe Differentialgeometrie |
| url | https://doi.org/10.1007/978-3-642-61981-6 |
| volume_link | (DE-604)BV020546983 |
| work_keys_str_mv | AT kobayashishoshichi transformationgroupsindifferentialgeometry |