On C3-like Finsler spaces (Q5903672)

By paying attention to the special form of the C-tensor \(C_{ijk}\) of a three-dimensional Finsler space, \textit{S. Numata} introduced the concept of C3-like Finsler space of dimension more than three [Rep. Math. Phys. 18, 1-10 (1980; Zbl 0536.53030)]. The C3-likeness of the present authors differs a little from Numata's: A Finsler space of dimension more than three is called C3-like if \(C_{ijk}=(h_{ij}a_ k+h_{jk}a_ i+h_{ki}a_ j)+(C_ iC_ jb_ k+C_ jC_ kb_ i+C_ kC_ ib_ j)\) where \(h_{ij}\) is the angular metric tensor and \(C_ i=C^ j_{ij}\).