芬斯拉度量的一般提升

General Lifts of Finsler Metrics

本文把Matsumoto提出的芬斯拉基本张量g到切丛的α提升推广成一般提升,其N-分解为满足α_(αβ)=α_(βα)。对于加当联络的情形,证明了使芬斯拉型线性联络关于为度量的充要条件是α_(αβ)均为常数。当取α_(11)=α_(22)=0时,所得应变张量场N-分解的8个芬斯拉张量场中有5个不为零,且都是正齐次的,最后还指出,只有这种取法才能获得正齐次的N-分解张量场。

In this paper we generalize the concept of α-lift of Finsler metrics presented in Matsumoto. We get all the eight Finsler tensor fields in the N-decompositions of the strain tensor field S produced through the general lift. By a suitable choice of constants, there appear five non-zero tensor fields which all are positive homogeneous.