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$(\alpha,\beta)$-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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[1] D. Bao, C. Robles, Z. Shen, Zermelo navigation on Riemannian manifolds, J. Diff. Geom., 66(3) (2004) 377-435.
[2] S. Basco, X. Cheng, Z. Shen, Curvature properties of (α, β)-metrics, In “Finsler Geometry, Sapporo 2005-In Memory of Makoto Matsumoto”, ed. S. Sabau and H. Shimada, Advanced Studies in Pure Mathematics 48, Mathematical Society of Japan, (2007) 73-110.
[3] V. N. Berestovskii , Yu. G. Nikonorov, Killing vector fields of constant length on Riemannian manifolds, (Russian) Sibirsk. Mat. Zh. 49(3) (2008) 497-514; translation in Sib. Math. J., 49(3) (2008) 395-407.
[4] B. Li, Z. Shen, On Randers metrics of quadratic Riemannian curvature, Internat. J. Math., 20(3) (2009) 369-376.
[5] M. Matsumoto, Foundations of Finsler geometry and special Finsler spaces, Kaiseisha, Japan, 1986.
[6] B. Rezaei, A. Razavi, N. Sadeghzadeh, On Einstein (α, β)-metrics, Iranian Journal of Science and Technology, 31 (2007) 403-412. | ||
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