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On Zermelo’s navigation problem and weighted Einstein Randers metrics | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 7، دوره 6، شماره 3، مهر 2025، صفحه 269-277 اصل مقاله (369.08 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2024.22745.1189 | ||
| نویسندگان | ||
| Illatra Khamonezhad؛ Bahman Rezaei* ؛ Mehran Gabrani | ||
| Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran | ||
| چکیده | ||
| This paper investigates a specific form of weighted Ricci curvature known as the quasi-Einstein metric. Two Finsler metrics, F and F˜ are considered, which are generated by navigation representations (h, W) and (F, V ), respectively, where W represents a vector field, and V represents a conformal vector field on the manifold M. The main focus is on identifying the necessary and sufficient condition for the Randers metric F to qualify as a quasi-Einstein metric. Additionally; we establish the relationship between the curvatures of the given Finsler metrics F and F˜. | ||
| کلیدواژه‌ها | ||
| Weighted Ricci curvature؛ Navigation problem؛ Conformal vector field | ||
| مراجع | ||
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[1] Xinyue Chen and Zhongmin Shen. Randers metrics with special curvature properties. Osaka J. Math., 40(1):87– 101, 2003.
[2] Xinyue Cheng and Hong Cheng. The characterizations on a class of weakly weighted Einstein-Finsler metrics. J. Geom. Anal., 33(8):Paper No. 267, 23, 2023.
[3] Xinyue Cheng, Hong Cheng, and Xibin Zhang. Some volume comparison theorems on Finsler manifolds of weighted Ricci curvature bounded below. J. Finsler Geom. Appl., 3(2):1–12, 2022.
[4] Xinyue Cheng, Qiuhong Qu, and Suiyun Xu. The navigation problems on a class of conic Finsler manifolds. Differential Geom. Appl., 74:Paper No. 101709, 13, 2021.
[5] Xinyue Cheng and Zhongmin Shen. Finsler geometry. Science Press Beijing, Beijing; Springer, Heidelberg, 2012. An approach via Randers spaces.
[6] M. Gabrani, B. Rezaei, and A. Tayebi. On projective Ricci curvature of Matsumoto metrics. Acta Math. Univ. Comenian. (N.S.), 90(1):111–126, 2021.
[7] Laya Ghasemnezhad, Bahman Rezaei, and Mehran Gabrani. On isotropic projective Ricci curvature of Creducible Finsler metrics. Turkish J. Math., 43(3):1730–1741, 2019.
[8] L. Kang. On conformal fields of (α, β)-spaces. Preprint, 2011.
[9] B. Najafi, Z. Shen, and A. Tayebi. Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties. Geom. Dedicata, 131:87–97, 2008.
[10] Shin-ichi Ohta. Finsler interpolation inequalities. Calc. Var. Partial Differential Equations, 36(2):211–249, 2009.
[11] Shin-ichi Ohta. Comparison Finsler geometry. Springer Monographs in Mathematics. Springer, Cham, 2021.
[12] M. Rafie-Rad and B. Rezaei. On Einstein Matsumoto metrics. Nonlinear Anal. Real World Appl., 13(2):882– 886, 2012.
[13] B. Rezaei, A. Razavi, and N. Sadeghzadeh. On Einstein (α, β)-metrics. Iran. J. Sci. Technol. Trans. A Sci., 31(4):403–412, 2007.
[14] Colleen Robles. Einstein metrics of Randers type. PhD thesis, The University of British Columbia (Canada), 2003.
[15] Zhongmin Shen. Volume comparison and its applications in Riemann-Finsler geometry. Adv. Math., 128(2):306– 328, 1997.
[16] Zhongmin Shen. Differential geometry of spray and Finsler spaces. Kluwer Academic Publishers, Dordrecht, 2001.
[17] Zhongmin Shen and Liling Sun. On the projective Ricci curvature. Sci. China Math., 64(7):1629–1636, 2021.
[18] ZhongMin Shen and QiaoLing Xia. On conformal vector fields on Randers manifolds. Sci. China Math., 55(9):1869–1882, 2012.
[19] Zhongmin Shen and Changtao Yu. On Einstein square metrics. Publ. Math. Debrecen, 85(3-4):413–424, 2014.
[20] Zhongmin Shen and Runzhong Zhao. On a class of weakly weighted Einstein metrics. Internat. J. Math., 33(10-11):Paper No. 2250068, 15, 2022.
[21] Tayebeh Tabatabaeifar and Behzad Najafi. (α, β)-metrics with killing β of constant length. AUT J. Math. Comput., 1(1):27–36, 2020.
[22] Tayebeh Tabatabaeifar, Behzad Najafi, and Akbar Tayebi. Weighted projective Ricci curvature in Finsler geometry. Math. Slovaca, 71(1):183–198, 2021.
[23] Akbar Tayebi and Ali Nankali. On generalized Einstein Randers metrics. Int. J. Geom. Methods Mod. Phys., 12(10):1550105, 14, 2015.
[24] Akbar Tayebi and Mohammad Shahbazi Nia. A new class of projectively flat Finsler metrics with constant flag curvature K = 1. Differential Geom. Appl., 41:123–133, 2015.
[25] Hongmei Zhu. On a class of quasi-Einstein Finsler metrics. J. Geom. Anal., 32(7):Paper No. 195, 28, 2022. | ||
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