On Kropina Change of m-th Root Finsler Metrics

In this paper, we consider Kropina change of $m$-th root Finsler metrics. We find necessary and sufficient condition under which the Kropina change of an $m$-th root Finsler metric be locally dually flat. Then we prove that the Kropina change of an $m$-th root Finsler metric is locally projectively flat if and only if it is locally Minkowskian.Comment: accepted in Ukrainian Mathematical Journal Volume 66, number 1, 201

On a class of projectively flat Finsler metrics

In this paper, we study a class of Finsler metrics composed by a Riemann metric $\alpha=\sqrt{a_{ij}(x)y^i y^j}$ and a $1$-form $\beta=b_i(x)y^i$ called general ($\alpha$, $\beta$)-metrics. We classify those projectively flat when $\alpha$ 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

ON CONFORMAL-MATSUMOTO CHANGE OF m-TH ROOT FINSLER METRICS

In this paper, we have considered conformal-Matsumoto change of the class of m-th root Finsler metrics. We have established the necessary and sufficient condition for the transformed metric to be projectively flat or locally dually flat. Further, we have proved the non-existence of the concerned metric which is projectively flat with non-zero flag curvature