ON A CLASS OF LOCALLY PROJECTIVELY FLAT GENERAL (α, β)-METRICS

ON A CLASS OF LOCALLY PROJECTIVELY FLAT GENERAL (α, β)-METRICS

General (${\alpha},{\beta}$)-metrics form a rich class of Finsler metrics. They include many important Finsler metrics, such as Randers metrics, square metrics and spherically symmetric metrics. In this paper, we find equations which are necessary and sufficient conditions for such Finsler metric to be locally projectively flat. By solving these equations, we obtain all of locally projectively flat general (${\alpha},{\beta}$)-metrics under certain condition. Finally, we manufacture explicitly new locally projectively flat Finsler metrics.

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