On h-flat Finsler spaces (Q1070540)

The authors study the Finsler spaces \(F^ n\) endowed with a TMA- connection. If this connection satisfies the condition \(\bar R^ i_{jk}=0\) (resp. \(\bar R^ i_{hjk}=0)\) the space \(F^ n\) is called n-flat (resp. h-flat). An expression for the h-curvature tensor field \(\bar R^ i_{hjk}\) of a Finsler space \(F^ n\) with a TMA-connection is obtained and some characteristic conditions for h-flatness are given. The cases that the spaces \(F^ n\) are of constant curvature or isotropic are considered.