書誌事項
- タイトル別名
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- トウシツケイ ニ ツイテ 1 エイブン
- On Homogeneous Systems(I)
- トウシツケイ ニツイテ 1
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In this paper, homogeneous systems which have been introduced in [4] will be considered on differentiable manifolds. It is intended to show that the various results in [2], [3] for a homogeneous Lie loop G are essentially those results for the homogeneous system of G. Let (G, η) be a differentiable homogeneous system on a connected differentiable manifold G. The canonical connection and the tangent Lie triple algebra of (G, η) are defined in §§1, 2 in the same way as in the case of homogeneous Lie loops [2]. At any point e, G can be expressed as a reductive homogeneous space A/K with the canonical connection and with the decomposition 〓 = 〓 + 〓 of the Lie algebra of A , where 〓 is the tangent L. t. a. of (G, η) at e. In §3 we shall treat of the regular homogeneous system, a geodesic homogeneous system G in which the linear representation of K on 〓 coincides with the holonomy group at e. The following fact will be shown in §4 ; if (G, η) is a regular homogeneous system, then there exists a 1-1 correspondence between the set of invariant subsystem of G and the set of invariant subalgebras of its tangent L. t. a. (Theorem 5).
収録刊行物
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- Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences
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Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences 11 9-17, 1977-12-20
島根大学文理学部
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詳細情報 詳細情報について
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- CRID
- 1050845763441299072
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- NII論文ID
- 120005586731
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- NII書誌ID
- AN0010806X
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- ISSN
- 03709434
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- NDL書誌ID
- 1918302
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- 本文言語コード
- en
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- 資料種別
- departmental bulletin paper
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- データソース種別
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- IRDB
- NDL
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