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On weakly stretch Randers metrics. (English) Zbl 1488.53067

Summary: The class of weakly stretch Finsler metrics contains the class of stretch metric. Randers metrics are important Finsler metrics which are defined as the sum of a Riemann metric and a 1-form. In this paper, we prove that every Randers metric with closed and conformal one-form is a weakly stretch metric if and only if it is a Berwald metric.

MSC:

53B40 Local differential geometry of Finsler spaces and generalizations (areal metrics)
53C60 Global differential geometry of Finsler spaces and generalizations (areal metrics)
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References:

[1] M. Atashafrouz, B. Najafi, A. Tayebi,Weakly Douglas Finsler metrics, Periodica Math Hungarica.81(2020), 194-200. · Zbl 1474.53104
[2] S. B´acs´o, M. Matsumoto,On Finsler spaces of Douglas type, A generalization of notion of Berwald space, Publ. Math. Debrecen.51(1997), 385-406. · Zbl 0907.53045
[3] S. B´acs´o, M. Matsumoto,Finsler spaces with h-curvature tensorHdependent on position alone, Publ. Math. Debrecen.55(1999), 199-210. · Zbl 0973.53014
[4] S. B´acs´o, Z. Szilasi,On the direction independence of two remarkable Finsler tensors, Differ. Geom. Appl. Proc. Conf., in Honour of Leonhard Euler, Olomouc, August 2007, 397-406. · Zbl 1165.53014
[5] L. Berwald,Uber Parallel¨¨ubertragung in R¨aumen mit allgemeiner Massbestimmung, Jber. Deutsch. Math.-Verein.34(1926), 213-220. · JFM 52.0728.01
[6] X. Cheng, Z. Shen,Randers metric with special curvature properties, Osaka. J. Math.40 (2003), 87-101. · Zbl 1100.53056
[7] B. Li, Z. Shen,On Randers metrics of quadratic Riemann curvature, Int. J. Math.20(2009), 369-376. · Zbl 1171.53020
[8] M. Matsumoto,An improvment proof of Numata and Shibata’s theorem on Finsler spaces of scalar curvature, Publ. Math. Debrecen.64(2004), 489-500. · Zbl 1093.53030
[9] B. Najafi, B. Bidabad, A. Tayebi,On R-quadtratic Finsler metrics, Iran. J. Science, Tech. Trans A.31(2007), 439-443. · Zbl 1169.53319
[10] B. Najafi, A. Tayebi,Weakly stretch Finsler metrics, Publ. Math. Debrecen.91(2017),441- 454. · Zbl 1399.53033
[11] Z. Shen,Finsler metrics withK= 0andS= 0, Canadian J. Math.55(2003), 112-132. · Zbl 1035.53104
[12] C. Shibata,On the curvatureRhijkof Finsler spaces of scalar curvature, Tensor, N.S.32 (1978), 311-317. · Zbl 0411.53016
[13] C. Shibata,On Finsler spaces with Kropina metric, Rep. Math. Phys.13(1978), 117-128. · Zbl 0389.53008
[14] A. Tayebi,On the class of generalized Landsberg manifolds, Period. Math. Hungarica.72 (2016), 29-36. · Zbl 1374.53110
[15] A. Tayebi,On 4-th root Finsler metrics of isotropic scalar curvature, Math. Slovaca.70(2020), 161-172.
[16] A. Tayebi, N. Izadian,Douglas-square metrics with vanishing mean stretch curvature, Int. Electronic. J. Geom.12(2019), 188-201. · Zbl 1459.53036
[17] A. Tayebi, B. Najafi,Classification of 3-dimensional Landsbergian(α, β)-mertrics, Publ. Math. Debrecen.96(2020), 45-62. · Zbl 1463.53035
[18] A. Tayebi, B. Najafi,On a class of homogeneous Finsler metrics, J. Geom. Phys.140(2019), 265-270. · Zbl 1417.53024
[19] A. Tayebi, M. Razgordani,On H-curvature of(α, β)-metrics, Turkish. J. Math.44(2020), 207-222. · Zbl 1451.53036
[20] A. Tayebi, H. Sadeghi,On Cartan torsion of Finsler metrics, Publ. Math. Debrecen.82(2) (2013), 461-471. · Zbl 1299.53065
[21] A. Tayebi, H. Sadeghi,On a class of stretch metrics in Finsler geometry, Arab. J. Math.8 (2019), 153-160. · Zbl 1418.53080
[22] A. Tayebi, T. Tabatabaeifar,Douglas-Randers manifolds with vanishing stretch tensor, Publ. Math. Debrecen.86(2015), 423-432. · Zbl 1363.53022
[23] C. Yu,Douglas metrics of(α, β)-type, arXiv:1609.04109v1
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