Projective change between two classes \(of(\alpha ,\beta )\)-metrics (Q838023)

Within the framework of Finsler geometry, the paper determines for dimension \(n\geq3\) \ the equations which characterize the projective change between the \((\alpha,\beta)-\)metric \(F=(\alpha+\beta)^2/\alpha\) and the Randers metric \({\bar F}={\bar \alpha}+{\bar \beta}\), where \(\alpha\) and \({\bar\alpha}\) are Riemannian metrics and \(\beta,{\bar \beta}\) are nonzero one forms. This result extends another one obtained in [\textit{Z. Shen, G. Civi Yildirim}, Can. J. Math. 60, No. 2, 443--456 (2008; Zbl 1157.53014)]. As well, the projective change is studied in the case when \(F\) satisfies certain curvature properties.