On a special form of the \(h\nu\)-curvature tensor of Berwald's connection \(B\Gamma\) of Finsler space. II (Q1901629)

In their previous paper [Ind. J. Pure Appl. Math. 25, No. 12, 1275-1280 (1994; Zbl 0820.53034)] the authors have introduced a special form of the \(hv\)-curvature tensor \(G_h{}^i_{jk}\) of the Berwald connection. In the present paper, they propose another special form (B): \(G_h{}^i_{jk}= b^i C_{hjk}+ L^{- 1}\mu (h^i_h h_{jk} h^i_j h_{kh}+ h^i_k h_{hj})\). If a Finsler space is \(h\)-conformal to a Berwald space, then its \(hv\)-curvature tensor is of the form (B). If a Finsler space has \(G_h{}^i_{jk}\) of the form (B) and \(b^i\) is a \(h\)-vector field, then \(\mu\) is independent of \(y^i\) and its Douglas tensor is written in the form \(D_h{}^i_{jk}= (b^i- 2ay^i) C_{hjk}+ (L^{- 1}\mu- a)(h^i_h h_{jk}+ h^i_j h_{kh}+ h^i_k h_{hj})\).