On a Class of Singular Projectively Flat Finsler Metrics with Constant Flag Curvature

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Singular Finsler metrics, such as Kropina metrics and m-Kropina metrics, have a lot of applications in the real world. In this paper, we classify a class of singular (α,β)-metrics which are locally projectively flat with constant flag curvature in dimension n= 2 and n ≥ 3 respectively. Further, we determine the local structure of m-Kropina metrics and particularly Kropina metrics which are projectively flat with constant flag curvature and prove that such metrics must be locally Minkowskian but are not necessarily flat-parallel.