ID  35 
Author 
Ichijyo, Yoshihiro
Department of Mathematics College of General Education University of Tokushima

Content Type 
Departmental Bulletin Paper

Description  In the previous paper [5], the present author has treated Finsler manifolds with such a property that the tangent spaces at arbitrary points are congruent (isometrically linearly isomorphic) to a single Minkowski space, and introduced, as a typical example of such a space, the notion of {V, H}manifolds. At the same time, it has been shown that the {V, H}manifolds are generalized Berwald spaces defined by Hashiguchi [3] and Wagner [9]. Now, the present paper has two main purposes. One is to consider the converse of the abovementioned result. After some preparation, it will be proved, in §3, that if a generalized Berwald space is connected, it is actually a {V, H}manifold. Next, in a Minkowski space is presented a Riemann metric, which is different from the Minkowski norm. Therefore, geodesic lines with respect to this Riemann metric can be introduced in the Minkowski space, which we call Cgeodesics. A connected Finsler manifold M with a linear connection Γ^i_<jk>(x) is to be considered. With regard to arbitrary two points p and q in M and any piecewise differentiable curve C joining p and q, we can define a linear isomorphic mapping σ between the tangent Minkowski spaces Tp(M] and Tq(M) by parallel displacement with respect to Γ^i_<jk>(x) along the curve C. Now, the other main purpose of the present paper is to find a necessary and sufficient condition for a to map any Cgeodesic in Tp(M) to a Cgeodesic in Tq(M). It will be shown, in the last section, that the condition is C^i_<jkh>=0 or equivalently P^i_<jkh>=0 with respect to the Finser connection associated with the linear connection Γ^i_<jk>(x).

Journal Title 
Journal of mathematics, Tokushima University

ISSN  00754293

NCID  AA00701816

Volume  10

Start Page  1

End Page  11

Sort Key  1

Published Date  19761031

Remark  公開日:2010年1月24日で登録したコンテンツは、国立情報学研究所において電子化したものです。

FullText File  
language 
eng
