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 11 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  19771220

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

OAIPMH Set 
Faculty of Science and Engineering
