On special forms of \(C_{i| j}\) and \(T_{ij}\) in Finsler spaces (Q1120127)

The purpose of the present paper is to study Finsler spaces having the torsion tensor \(C_ i\) such that \(C_{i| j}\) is proportional to the angular metric tensor \(h_{ij}\) and those having the contracted T-tensor \(T_{ij}\) proportional to the same tensor. For example, in an S3-like Finsler space \((L^ 2S_{hijk}=S(h_{hj}h_{ik}-h_{hk}h_{ij}))\) satisfying \(T_{ij}=\mu h_{ij}\), the scalar function \((S+1)\log \sqrt{g}+\mu L\) is a function of position alone.