Natural Operations in Differential Geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1993
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M. |
| Beschreibung: | 1 Online-Ressource (VI, 434 p) |
| ISBN: | 9783662029503 9783642081491 |
| DOI: | 10.1007/978-3-662-02950-3 |
Internformat
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| 100 | 1 | |a Kolář, Ivan |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Natural Operations in Differential Geometry |c by Ivan Kolář, Jan Slovák, Peter W. Michor |
| 264 | 1 | |a Berlin, Heidelberg |b Springer Berlin Heidelberg |c 1993 | |
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| 500 | |a The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M. | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Kolář, Ivan |
| author_facet | Kolář, Ivan |
| author_role | aut |
| author_sort | Kolář, Ivan |
| author_variant | i k ik |
| building | Verbundindex |
| bvnumber | BV042423228 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)1184493183 (DE-599)BVBBV042423228 |
| 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 | 10.1007/978-3-662-02950-3 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662029503 9783642081491 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027858645 |
| oclc_num | 1184493183 |
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| physical | 1 Online-Ressource (VI, 434 p) |
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| publishDate | 1993 |
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| publisher | Springer Berlin Heidelberg |
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| spelling | Kolář, Ivan Verfasser aut Natural Operations in Differential Geometry by Ivan Kolář, Jan Slovák, Peter W. Michor Berlin, Heidelberg Springer Berlin Heidelberg 1993 1 Online-Ressource (VI, 434 p) txt rdacontent c rdamedia cr rdacarrier The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M. Mathematics Global differential geometry Quantum theory Differential Geometry Quantum Information Technology, Spintronics Quantum Physics Mathematik Quantentheorie Normaler Operator (DE-588)4304687-3 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 s Normaler Operator (DE-588)4304687-3 s 1\p DE-604 Slovák, Jan Sonstige oth Michor, Peter W. Sonstige oth https://doi.org/10.1007/978-3-662-02950-3 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Kolář, Ivan Natural Operations in Differential Geometry Mathematics Global differential geometry Quantum theory Differential Geometry Quantum Information Technology, Spintronics Quantum Physics Mathematik Quantentheorie 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 by Ivan Kolář, Jan Slovák, Peter W. Michor |
| title_fullStr | Natural Operations in Differential Geometry by Ivan Kolář, Jan Slovák, Peter W. Michor |
| title_full_unstemmed | Natural Operations in Differential Geometry by Ivan Kolář, Jan Slovák, Peter W. Michor |
| title_short | Natural Operations in Differential Geometry |
| title_sort | natural operations in differential geometry |
| topic | Mathematics Global differential geometry Quantum theory Differential Geometry Quantum Information Technology, Spintronics Quantum Physics Mathematik Quantentheorie Normaler Operator (DE-588)4304687-3 gnd Differentialgeometrie (DE-588)4012248-7 gnd |
| topic_facet | Mathematics Global differential geometry Quantum theory Differential Geometry Quantum Information Technology, Spintronics Quantum Physics Mathematik Quantentheorie Normaler Operator Differentialgeometrie |
| url | https://doi.org/10.1007/978-3-662-02950-3 |
| work_keys_str_mv | AT kolarivan naturaloperationsindifferentialgeometry AT slovakjan naturaloperationsindifferentialgeometry AT michorpeterw naturaloperationsindifferentialgeometry |