DSpace DSpace 日本語

長崎県立大学学術リポジトリ >
国際情報学部研究紀要:第1号~第16号 >
第12号 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10561/702

Title: A note on linear parallel displacements in Finsler geometry
Author: 永野, 哲也
Author's alias: NAGANO, Tetsuya
Issue Date: 22-Dec-2011
Publisher: 長崎県立大学
Shimei: 研究紀要
Issue: 12
Start page: 195
End page: 205
ISSN: 1883-8111
Abstract: The author stated the notion of parallel displacements of vector fields along a curve on the 43-rd Symposium on Finsler geometry at Utsunomiya, 2008. The definition is linear with respect to a vector field. So the author redefines it as "linear" parallel displacement followed in [2](In this book, however, linear parallel displacements are defined by an non-linear connection N).On the other hand, the traditional ways of the definition is not linear with respect to a vector field([1]).Further in the early stages of Finsler geometry, many authors gave its definitions([3])and in the book [4]they were collected. In all cases, however, the studies that the author states in this paper were not investigated. In the first half of section 1, the same contents to [7] and [8] with a little difference are stated and in the second half the necessary and sufficient condition that linear parallel displacements are symmetric for any path is stated. In section 2, the determinant of Φ derived from linear parallel displacements is given and cases that Φ is Identity transformation and an orthogonal one are stated. The terminology and notations are referred to the books [5] and [6]. The author is given very useful suggestions by Prof.T.Aikou and Prof.M.Hashiguchi frequently, and greatly appreciates their kindness.
Keywords: linear parallel displacement, path, Finsler spaces.
URI: http://hdl.handle.net/10561/702
Appears in Collections:第12号

Files in This Item:

File Description SizeFormat
v12p195_nagao.pdf3.35 MBAdobe PDFView/Open

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Nagasaki Prefectural University attached library