On a class of locally projectively flat Finsler metrics (II) (Q1733240)

The authors investigate an interesting class of Finsler metrics, namely the general \((\alpha, \beta)\)-metrics. This class of metrics are defined as we know by a Riemannian metric \(\alpha\) and a 1-form \(\beta\). The authors give an equivalent characterization of locally projectively flat general \((\alpha, \beta)\)-metrics on an \(n\)-dimensional manifold, \(n\geq 3\), which generalizes some well-known results, and also, they obtain a series of new locally projectively flat Finsler metrics. The paper consist of 5 sections. In Section 4, the authors find some necessary conditions for general \((\alpha, \beta)\)-metrics to be locally projectively flat. In conclusion, the paper is interesting, the authors obtains new and interesting results in Finsler geometry, very useful in the study of the general \((\alpha, \beta)\)-metrics.