On a class of projectively flat Finsler metrics (Q901063)

The author classifies locally projectively flat general \((\alpha,\beta)\)-metrics of the form \(F=\alpha\varphi(b^2,\frac{\beta}{\alpha})\) on an \(n\)-dimensional manifold, \(n\geqslant 3\), for the case when \(\alpha\) is of constant sectional curvature and \(\varphi_1\neq 0\), i.e., \(\varphi\) essentially depends on its first argument. Furthermore, the equations which characterize this class of metrics with constant flag curvature are found, and their local structures are determined.