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Title Transcription
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
Title Alternative (English)
System of Local Loops on a Manifold and Affine Connection
File
language
eng
Author
Kikkawa, Michihiko
Description
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).
Journal Title
島根大学論集. 自然科学
Volume
16
Start Page
12
End Page
14
ISSN
04886542
Published Date
1966-12-25
NCID
AN0010814X
Publisher
島根大学
Publisher Aalternative
Shimane University
NII Type
Departmental Bulletin Paper
OAI-PMH Set
Faculty of Science and Engineering
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