Classification of three-dimensional left-invariant Ricci-quadratic Randers metrics and their applications

Najafi, Behzad; Tayebi, Akbar; Barati, Fatemeh

doi:10.22034/cmde.2025.66684.3141

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	45
تعداد شماره‌ها	1,554
تعداد مقالات	18,950
تعداد مشاهده مقاله	63,892,161
تعداد دریافت فایل اصل مقاله	23,341,337

	Classification of three-dimensional left-invariant Ricci-quadratic Randers metrics and their applications
Computational Methods for Differential Equations
مقاله 11، دوره 14، شماره 4، دی 2026، صفحه 1698-1712 اصل مقاله (446.37 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.66684.3141
نویسندگان
Behzad Najafi^* ¹؛ Akbar Tayebi²؛ Fatemeh Barati²
¹Department of Mathematics and Computer Sciences, Amirkabir University of Technology (Tehran Polytechnic), Tehran. Iran.
²Department of Mathematics, Faculty of Science, University of Qom. Qom. Iran.
چکیده
In this paper, we determine the necessary and sufficient conditions for a left-invariant Randers metric to be a Ricci-quadratic metric. Then, by using HaBumlee’s classification of left-invariant Riemannian metrics and our characterization of Ricci-quadratic left-invariant Randers metrics, we give the classification of left-invariant Ricci-quadratic Randers metrics on three-dimensional Lie groups. As an application, we find an interesting Ricci-quadratic Randers metric on $SU(2)$ which is a generalized Berwald metric, while it is not Berwaldian. Also, we prove that it is a generalized Douglas-Weyl metric which is neither Douglasian nor a Weyl metric.
کلیدواژه‌ها
Left-invariant metric؛ Randers metric؛ Ricci-quadratic metric؛ Berwald metric

مراجع
[1] M. Atashafrouz and B. Najafi, On Cheng-Shen conjecture in Finsler geometry, Int. J. Math., 31 (2020), 2050030. [2] S. Bàcsò and M. Matsumoto, Finsler spaces with h-curvature tensor H dependent on position alone, Publ. Math. Debrecen., 55 (1999), 199-210. [3] S. Bàcsò and M. Matsumoto, On Finsler spaces of Douglas type, A generalization of notion of Berwald space, Publ. Math. Debrecen., 51 (1997), 385-406. [4] S. Bàcsò and M. Matsumoto, On Finsler spaces of Douglas type II. Projectively flat spaces, Publ. Math. Debrecen., 53 (1998), 423-438. [5] D. Bao and C. Robles, Ricci and Flag curvatures in Finsler geometry, A Sampler of Riemann-Finlser Geometry, MSRIP., 50 (2004), 198-256. [6] X. Cheng and Z. Shen, Finsler Geometry, An Approach via Randers Spaces, Springer, 2012. [7] S. Deng, Homogeneous Finsler Spaces, Springer, 2012. [8] S. Deng, Invariant Randers metrics on homogeneous Riemannian manifolds, J. Phys. A: Math. Gen., 37 (2004), 4353-4360. [9] M. Gabrani, B. Rezae, and E. S. Sevim. On m-th root metrics of isotropic projective Ricci curvature, AUT J. Math. Comput., 4(2) (2023) 123-128. [10] K. Y. Ha and J. Bumlee, Left invariant metrics and curvatures on simply connected three-dimensional Lie groups, Math. Nachr., 282(6) (2009), 868-898. [11] S. Helgason, Differential Geometry, Lie Groups and Symmetric Spaces, Academic, New York, (1978). [12] Z. Hu and S. Deng, Ricci-quadratic homogeneous Randers spaces, Nonlinear Analysis., 92 (2013), 130-137. [13] B. Li and Z. Shen, Randers metrics of quadratic Riemann curvature, Int. J. Math., 20 (2009), 1-8. [14] M. Matsumoto and S. H¯oj¯o, A conclusive theorem for C-reducible Finsler spaces, Tensor. N. S., 32 (1978), 225-230. [15] J. Milnor, Curvatures of left invariant metrics on Lie groups, Adv. Math. 21 (1976), 293-329. [16] C. Robles, Einstein metrics of Randers type, Doctoral Dissertation, University of British Columbia, 2003. [17] N. Sadeghzadeh, On projective Riemann quadratic (PR-quadratic) Finsler metrics, J. Finsler Geom. Appl., 5(1) (2024), 115-126. [18] N. Sadeghzadeh and N. Sajjadi Moghadam, On special class of R-quadratic Finsler metrics, J. Finsler Geom. Appl., 4(1) (2023), 45-54. [19] Z. Shen, On R-quadratic Finsler Spaces, Publ. Math. Debrecen. 52(1-2) (2001), 263-274. [20] Z. Shen, Finsler metrics with K = 0 and S = 0, Canadian J. of Math., 55(1) (2003), 112-132. [21] Z. Shen, Weighted Ricci curvature in Riemann-Finsler geometry, AUT J. Math. Comput., 2(2) (2021) 117-136. [22] A. Tayebi and M. Barzegari, Generalized Berwald spaces with (α, β)-metrics, Indagationes. Math. (N.S.), 27(2016), 670-683. [23] A. Tayebi and F. Eslami, On a class of generalized Berwald manifolds, Publ. Math. Debrecen., 105 (2024), 379-402. [24] A. Tayebi and B. Najafi, A class of homogeneous Finsler metrics, J. Geom. Phys., 140 (2019), 265-270. [25] A. Tòth and Z. Kovàcs, Left invariant Randers metrics on the 3-dimensional Heisenberg group, Publ. Math. Debrecen., 85 (2014), 161-179. [26] C. Vincze, On Randers manifolds with semi-symmetric compatible linear connections, Indagationes. Math. (N.S.), 26 (2015), 363-379. [27] M. Xu and S. Deng, Kiling frames and S-curvature of homogeneous Finsler spaces, Glasgow. Math. J., 57 (2015), 457-464. [28] L. Zhang and L. Huang, Three-dimensional Lie groups of scalar Randers type, Annali di Matematica Pura ed Applicata, (2023).
آمار تعداد مشاهده مقاله: 395 تعداد دریافت فایل اصل مقاله: 333

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Classification of three-dimensional left-invariant Ricci-quadratic Randers metrics and their applications