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Title Transcription
トウシツケイ ニツイテ 1
Title Alternative
On Homogeneous Systems(I)
File
language
eng
Author
Kikkawa, Michihiko
Description
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).
Journal Title
Memoirs of the Faculty of Literature and Science, Shimane University. Natural sciences
Volume
11
Start Page
9
End Page
17
ISSN
03709434
Published Date
1977-12-20
NCID
AN0010806X
Publisher
島根大学文理学部
Publisher Aalternative
The Faculty of Literature and Science, Shimane University
NII Type
Departmental Bulletin Paper
OAI-PMH Set
Faculty of Science and Engineering