On Finsler spaces of constant curvature (Q1074124)

For a Finsler space \(F^ n\), the authors consider a tensor W which differs from H, the h(hh)-curvature of the Berwald connection, by an additional term constructed by using \(H_{jk}=H^ i_{jki}\). They show that W is invariant under a C-projective mapping and prove that \(F^ n\) is of constant curvature if and only if \(W=0\). Two technical conditions for a Finsler space of scalar curvature to be a Finsler space of constant curvature are established, too.