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

	$(\alpha,\beta)$-Metrics with killing $\beta$ of constant length
AUT Journal of Mathematics and Computing
مقاله 3، دوره 1، شماره 1، اردیبهشت 2020، صفحه 27-36 اصل مقاله (466.7 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2018.3038
نویسندگان
Tayebeh Tabatabaeifar؛ Behzad Najafi^*
Department of Mathematics and Computer Science, Amirkabir University of Technology, 424, Hafez Ave., Tehran 15914, Iran
چکیده
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.
کلیدواژه‌ها
Finsler metric؛ $(\alpha,\beta)$-metric؛ Einstein manifold
مراجع

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