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Higher-Order Preconnections in Synthetic Differential Geometry of Jet Bundles
http://hdl.handle.net/2241/100309
http://hdl.handle.net/2241/10030982f235fe-fe30-4a7f-a08a-d135ecfdea84
名前 / ファイル | ライセンス | アクション |
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BAG_45-2.pdf (1.9 MB)
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Item type | Journal Article(1) | |||||
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公開日 | 2008-08-25 | |||||
タイトル | ||||||
タイトル | Higher-Order Preconnections in Synthetic Differential Geometry of Jet Bundles | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | journal article | |||||
著者 |
Nishimura, Hirokazu
× Nishimura, Hirokazu |
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著者別名 |
西村, 泰一
× 西村, 泰一 |
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抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | In our previous papers (Nishimura [2001 and 2003]) we dealt with jet bundles from a synthetic perch by regarding a 1-jet as something like a pinpointed (nonlinear) connection (called a preconnection) and then looking on higher-order jets as repeated 1-jets. In this paper we generalize our notion of preconnection to higher orders, which enables us to develop a non-repetitive but still synthetic approach to jet bundles. Both our repetitive and non-repetitive approaches are coordinate-free and applicable to microlinear spaces in general. In our non-repetitive approach we can establish a theorem claiming that the $(n+1)$-th jet space is an affine bundle over the $n$-th jet space, while we have not been able to do so in our previous repetitive approach. We will show how to translate repeated 1-jets into higher-order preconnections. Finally we will demonstrate that our repetitive and non-repetitive approaches to jet bundles tally, as far as formal manifolds are concerned. | |||||
書誌情報 |
Beiträge zur Algebra und Geometrie 巻 45, 号 2, p. 677-696, 発行日 2004 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 0138-4821 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AA00558880 | |||||
権利 | ||||||
権利情報 | © 2004 Heldermann Verlag | |||||
著者版フラグ | ||||||
値 | author | |||||
出版者 | ||||||
出版者 | Heldermann Verlag | |||||
URI | ||||||
識別子 | http://hdl.handle.net/2241/100309 | |||||
識別子タイプ | HDL | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf |