タイトルヨミ | タヨウタイジョウ ノ キョクショ ループケイ ト アフィン セツゾク
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日本語以外のタイトル | System of Local Loops on a Manifold and Affine Connection
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ファイル | |
言語 |
英語
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著者 |
吉川 通彦
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内容記述(抄録等) | The concepts of topological loops (Hofmann [2]) and analytic loops (Malcev [5]) lead us to the concept of differentiable local loops (§ 2, Definition 1) and local loops on manifolds have been studied by the author ([3]). Namely, in a differentiable manifold with an affine connection, each point has a neighbourhood which is a differentiable local loop with a binary operation defined by means of the parallel displacement of geodesics ([3] Theorem 1).
In the present paper, differentiable manifold with a system which assigns to each point a neighbourhood with a structure of local loop will be introduced (§ 2, Definition 2) and it will be shown that an affine connection of a manifold is determined by such a system (§ 3, Theorem 1). In particular, it will be proved that if a differentiable manifold M with an affine connection г is given then г coincides with the affine connection г_∑ of M which is determined by the system ∑ of local loops associated with г (Theorem 2). |
掲載誌名 |
島根大学論集. 自然科学
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巻 | 16
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開始ページ | 12
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終了ページ | 14
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ISSN | 04886542
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発行日 | 1966-12-25
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NCID | AN0010814X
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出版者 | 島根大学
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出版者別表記 | Shimane University
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資料タイプ |
紀要論文
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部局 |
総合理工学部
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他の一覧 |