On symmetric Finsler spaces of \(H_ p\)-scalar curvature and scalar curvature (Q1085449)

A Finsler space \(F_ n\) is said to be of Hp-scalar curvature if \(p\cdot H_{\ell ijr}=k(h_{\ell j} h_{ir}-h_{\ell r} h_{ij})\), where \(H_{\ell ijr}\) is the Berwald h-curvature tensor, p is an operator projecting on the indicatrix, \(h_{ij}\) is the angular metric tensor, and k is the curvature scalar. It is proved that for any Berwald space of Hp-scalar curvature \(p\circ H_ i^{\ell}{}_{jr| m}=0\) (\(|\) denoting the h-covariant derivative for the Cartan connection). Some other theorems concerning symmetric \(F_ n\) of Hp-scalar curvature resp. of scalar curvature are given.