On a special form of the \(hv\)-curvature tensor of Berwald's connection \(B\Gamma\) of Finsler space (Q1345198)

Let \(G_ h{}^ i{}_{jk}\) be the \(hv\)-curvature tensor of the Berwald connection of a Finsler space. Suggested by the special form of \(G_ h{}^ i{}_{jk}\) in the two-dimensional case, the authors consider Finsler spaces with \(G_ h{}^ i{}_{jk}\) of the form \[ G_ h{}^ i{}_{jk} = \{(a_ hy^ i + \lambda h^ i{}_ h)h_{jk} + (h,j,k)\}. \] If such a space is a Landsberg space, then we have \(a_ i = 0\). In the case \(n > 2\), \(\lambda L\) does not depend on \(y^ i\). If \(\lambda \neq 0\) identically, then the Douglas tensor vanishes and the space is a \(C\)- reducible Finsler space with \(a_ i = 2\lambda C_ i/(n + 1)\).