%0 Journal Article
%T $(\alpha,\beta)$-Metrics with killing $\beta$ of constant length
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Tabatabaeifar, Tayebeh
%A Najafi, Behzad
%D 2020
%\ 02/01/2020
%V 1
%N 1
%P 27-36
%! $(\alpha,\beta)$-Metrics with killing $\beta$ of constant length
%K Finsler metric
%K $(\alpha,\beta)$-metric
%K Einstein manifold
%R 10.22060/ajmc.2018.3038
%X The class of $(\alpha,\beta)$-metrics is a rich and important class of Finsler metrics, which is extensively studied. Here, we study $(\alpha,\beta)$-metrics with Killing of constant length $1$-form $\beta$ and find a simplified formula for their Ricci curvatures. Then, we show that if $F=\alpha+\alpha\beta+b\frac{{\beta}^2}{\alpha}$ is an Einstein Finsler metric, then $\alpha$ is an Einstein Riemann metric.
%U https://ajmc.aut.ac.ir/article_3038_ec3b89402c7338eacb774d68fb1a1cb0.pdf