$(\alpha,\beta)$-Metrics with killing $\beta$ of constant length

Document Type : Original Article


1 Amirkabir university

2 Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic)


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.


Main Subjects

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