On metrical Finsler connections with torsion of generalized Finsler spaces (Q1327660)

It is proved that the space \((M,g_{ij})\) with the metrical connection \(\mathring C\Gamma(N^ i_ k, F^ i_{jk},C^ i_{jk})\) has the property \(F^ i_{jk}= F^ i_{jk}(x)\) iff \(C_{ijkl}= 0\) and \(T^ i_{jk}= T^ i_{jk}(x)\) \((T^ i_{jk}= F^ i_{jk}- F^ i_{kj})\). The methods used here are the same as in \textit{S. Kikuchi} [On metrical Finsler connections of generalized Finsler spaces, Finsler and Lagrange spaces, Proc. 5th Natl. Semin., Hon. 60th Birthday R. Miron, Brasov/Rom. 1988, 197-206 (1988; Zbl 0674.53037)], where beside many other interesting results the problem for \(T^ i_{jk}= 0\) was solved.