\(C^ V\)-symmetric Finsler spaces (Q1071324)

A Finsler space \(F_ n\) is called \(C^ V\)-symmetric if \(C_{ijk| \ell | m}=C_{ijk| m| \ell}\), where \(C_{ijk}(x,y)\) is the Cartan torsion tensor, and \(|\) denotes the V-covariant derivation (covariant derivation by \(y^ i)\). It is shown that a C-reducible and \(C^ V\)-symmetric \(F_ n\) is a Riemannian space \(V_ n\). As a consequence of this a \(C^ V\)-symmetric Randers-, or Kropina-space is also a \(V_ n\).