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

Document Type : Original Article

Authors

Department of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Ave., Tehran 15914, Iran

Abstract

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.

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References

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AUT Journal of Mathematics and Computing
Volume 1, Issue 1
February 2020
Pages 27-36

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