On \(C_ 3\)-like Finsler spaces (Q1900700)

A Finsler space \(F^n\) \((n\geq 4)\) is called \(C_3\)-like if the \(C\)- torsion tensor is of the form \(C_{ijk}= h_{ij} a_k+ C_i C_j b_k+ (ijk)\) for some \(a_k\) and \(b_k\), where \((ijk)\) denotes the cyclic permutation of \(i\), \(j\), \(k\) and summation. If \(2b_i C^i =1\), then the space is of a generalized \(C\)-reducible form: \(C_{ijk}= P_{ij} Q_k+ (ijk)\). If \(2b_i C^i\neq 1\), then \(C_{ijk}\) reduces to \((*)\) \(C_{ijk}= (Q_{ij} a_k+ (ijk))+ d_i d_j d_k\). If a Finsler space \((M^n, L(x, y))\) is \(C\)-reducible, then \(C_{ijk}\) of the space \((M^n, L^* (x, y))\) where \((L^*)^3= L^3+ (b_i (x) y^i)^3\) can be written in the form \((*)\).