On a class of projectively flat Finsler metrics

الأصل · EN

In this paper, we study a class of Finsler metrics composed by a Riemann metric α=√aij(x)yⁱ yʲ and a 1-form β=bᵢ(x)yⁱ called general (α, β)-metrics. We classify those projectively flat when α is projectively flat. By solving the corresponding nonlinear PDEs, the metrics in this class are totally determined. Then a new group of projectively flat Finsler metrics is found.