An algebraic characterisation for Finsler metrics of constant flag curvature (Q2042139)

This paper contains new and interesting results regarding the flag curvature of a Finsler metric. More exactly, the authors have proved that a Finsler metric has constant flag curvature if and only if the curvature of the induced nonlinear connection satisfies an algebraic identity with respect to some arbitrary second rank tensors. The flag curvature is an important tool in Finsler geometry and it is the generalization of sectional curvature from Riemannian geometry. The classification of Finsler metrics of constant flag curvature seems to be far from being solved. So, the topic of this paper which is also dedicated to the study of flag curvature is of big importance for those interested in the study of Finsler metrics. In the first main result of the paper, namely Theorem 1.1, the authors give an interesting algebraic characterisation for Finsler metrics of constant flag curvature. The second section of the paper is entitled Finsler metrics and their curvature tensors. Finally, in Section 3 of the paper, the authors prove Theorem 1.1, using Lemma 3.1 which characterises Finsler metrics of constant flag curvature.