$(α,β)$-Metrics with killing $β$ of constant length - Tayebeh Tabatabaeifar; Behzad Najafi (AUT Journal of Mathematics and Computing, 2020)
The class of $(α,β)$-metrics is a rich and important class of Finsler metrics, which is extensively studied. Here, we study $(α,β)$-metrics with Killing of constant length $1$-form $β$ and find a simplified formula for their Ricci curvatures. Then, we show that if $F=α+αβ+b\frac{β^2}{α}$ is an Einstein Finsler metric, then $α$ is an Einstein Riemann metric.