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1.
In 1980, H. Izumi [3] introduced the concept of an h-vector. For the Finsler space whose metric is transformed by an h-vector, B. N. Prasad [10] obtained the Cartan connection. On the other hand, M. Matsumoto [7] presented a systematic theory of Finslerian hypersurface. M. Kitayama [4] obtained certain results for the Finslerian hypersurface given by β-changes. The purpose of the present paper is to derive certain properties of a Finslerian hypersurface given by an h-vector. The terminologies and notations are referred to Matsumoto [8]. 相似文献
2.
We consider Finsler spaces with a Randers metric F=α+β, on the three dimensional real vector space, where α is the Euclidean metric and β=bdx
3
is a 1-form with norm b,0≤b<1. By using the notion of mean curvature for immersions in Finsler spaces introduced by Z. Shen, we get the ordinary differential
equation that characterizes the minimal surfaces of rotation around the x
3
axis. We prove that for every b,0≤b<1, there exists, up to homothety, a unique forward complete minimal surface of rotation. The surface is embedded, symmetric
with respect to a plane perpendicular to the rotation axis and it is generated by a concave plane curve. Moreover, for every
there are non complete minimal surfaces of rotation, which include explicit minimal cones.
Received: 30 November 2001 / Published online: 10 February 2003
RID="⋆"
ID="⋆" Partially supported by CAPES
RID="⋆⋆"
ID="⋆⋆" Partially supported by CNPq and PROCAD. 相似文献
3.
LetF n be a Finsler space with metric functionF(x, y). M. Matsumoto [6] has defined a modified Finsler spaceF n * whose metric functionF *(x, y) is given byF *2 = = F2 + (Xi(x)yi)2, whereX i are the components of a covariant vector which is a function of coordintae only. Since a concurrent vector is a function of coordinate only, Matsumoto and Eguchi [9] have studied various properties of the modified Finsler spaceF n * under the assumption thatX i are the components of a concurrent vector field inF n. In this paper we shall introduce the concept of semi-parallel vector field inF n and study the properties of modified Finsler spaceF n * . 相似文献
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6.
The conformai theory of Finsler spaces was initiated by Knebelman in 1929 and lately Kikuchi [7] gave the conditions for a
Finsler space to be conformai to a Minkowski space. However under theh-condition, the third author [4] obtained the conditions for a Finsler space to beh-conformal to a Minkowski space.
The purpose of the paper is to investigate the infinitesimalh-conformal motions of Finsler metric and its application to anH-recurrent Finsler space. We obtain the following results.
A. | Theorem 2.1. If an HR-F n space is a Landsberg space, then the tensorF hjk i is recurrent. | |
B. |
Proposition 3.3. An infinitesimalh-conformal motion satisfies
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