Total for the last 12 months
number of access : ?
number of downloads : ?
ID 46
Ichijyo, Yoshihiro Department of Mathematics, College of General Education, Tokushima University
Content Type
Departmental Bulletin Paper
The present paper is the continuation of the serial papers concerning the Finsler manifold modeled on a Minkowski space ([5], [6], [7]). A Finsler manifold whose tangent spaces at arbitrary points are congruent to a unique Minkowski space is called a Finsler manifold modeled on a Minkowski space. As an example of it, the notion of the {V, H}-manifold has been introduced in the paper [5]. On the other hand, M. Hashiguchi has defined a notion of a generalized Berwald space [2]. Following his definition, it is a Finsler manifold admitting a linear connection Γ(x) with respect to which ▽g=0 holds, where ▽ denotes the covariant derivative with respect to the Finsler connection (r'jk(x), rimk(x)ym). It has been shown, in the paper [5], that the [V, H}-manifold is a generalized Berwald space. In the paper [6] it has been proved that a standard generalized Berwald space is a {V, H}-manifold. And also it has been found, in the paper [7], that a Finsler manifold with a linear connection Γ(x) with respect to which ▽C=0 holds good becomes a {V, H}-manifold under some condition, where C is the tensor given by C^i_<jk>=1/2g^<im>∂mg_<jk>. Now, the main purpose of the present paper is to find the following two: The one is the condition for the {V, H}-manifold to be locally Minkowskian and the another is the condition for the {V, H}-manifold to be locally conformal to a Minkowski space. These will be shown in § 1 and § 2 using the terminology of the theory of G-structures. In section 3, examples of these manifolds will be shown especially in the case where the manifolds admit a Randers metric. The last section is devoted to consideration on the case that a Finsler manifold is globally conformal to a locally Minkowskian manifold.
Journal Title
Journal of mathematics, Tokushima University
Start Page
End Page
Sort Key
Published Date
FullText File