On conformally flat cubic \((\alpha,\beta)\)-metrics (Q2244677)

In their paper, the authors prove two main results concerning the cubic Finsler metric \(F(x,y)=\sqrt[3]{a_{ijk}(x)y^iy^jy^k}\) on an \(n\)-dimensional manifold \(M^n\). The first result is that on any conformally flat weakly Einstein cubic manifold \((M^n,F)\), where \(n\geq 3\), the metric \(F\) is either a Riemannian metric or a locally Minkowski one. The second result says that on every conformally flat cubic manifold \((M^n,F)\) with \(n\geq 3\) and of almost vanishing \(\Xi\)-curvature the metric \(F\) is also Riemannian or locally Minkowskian.