The Cartan tensor of a Finsler space with \(({\alpha{}}, {\beta{}}, {\gamma{}})\)metric (Q1803517)

The notion of generalized \(C\)-reducibility of a Finsler space was defined by \textit{T. Okada} and \textit{S. Numata} [Tensor, New Ser. 35, 313-318 (1981; Zbl 0473.53019)]. The authors define the more generalized \(C\)- reducibility as \(C_{ijk}=P_{ij}X_ k+Q_{ij}Y_ k+(i,j,k)\) where \((i,j,k)\) denotes cyclic sum in \(i,j,k\) and show that a Finsler space with a metric \(L(\alpha,\beta,\gamma)\) is more generalized \(C\)-reducible, where \(\alpha^ 2=a_{ij}(x)y^ iy^ j\), \(\beta^ 2=b_{ij}(x)y^ iy^ j\) and \(\gamma=f_ i(x)y^ i\).