پیوندهای مفید
آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 404 |
| تعداد مقالات | 3,549 |
| تعداد مشاهده مقاله | 5,503,572 |
| تعداد دریافت فایل اصل مقاله | 3,765,053 |
On generalized Berwald R-quadratic metrics | ||
| Journal of Hyperstructures | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 تیر 1404 اصل مقاله (1.61 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2025.16423.1065 | ||
| نویسندگان | ||
| Mohammad Mtashar Alzuhairy1؛ Bahman Rezaei* 2؛ Akbar Tayebi3 | ||
| 1department of mathematics, urmia university | ||
| 2Department of mathematics, Urmia University, Urmia , Iran | ||
| 3department of mathematics, qom university | ||
| چکیده | ||
| Every Riemannian metric is R-quadratic, while many Finsler metrics have not this property. A Finsler metric is called R-quadratic if its Riemannian curvature is quadratic in all direction at any points of the underlying manifold. A Finsler metric on a manifold is called a generalized Berwald metric if there exists a covariant derivative such that the parallel translations induced by it preserve the Finsler function. In this paper, we study the class of generalized Berwald (α, β)-manifolds with R-quadratic properties and prove a rigidity result. We show that such manifolds satisfy S=0 if and only if B=0. | ||
| کلیدواژه‌ها | ||
| Generalized Berwald manifold؛ locally dually flat metric؛ S-curvature | ||
| مراجع | ||
|
[1] S. B´acs´o and M. Matsumoto, Finsler spaces with h-curvature tensor H dependent on position alone, Publ. Math. Debrecen, 55(1999), 199-210. [2] D. Bao, S.S. Chern and Z. Shen, An Introduction to Riemann-Finsler Geometry, Springer, 2000. [3] D. Bao and Z. Shen, Finsler metrics of constant positive curvature on the Lie group S3, J. London. Math. Soc. 66(2002), 453-467. [4] X. Cheng, The (α, β)-metrics of scalar flag curvature, Differ. Geom. Appl, 35(2014), 361-369. [5] X. Cheng and Z. Shen, A class of Finsler metrics with isotropic S-curvature, Israel J. Math. 169(2009), 317-340. [6] X. Cheng, Z. Shen and Y. Zhou, On a class of locally dually flat Finsler metrics, Int. J. Math. 21(11) (2010), 1-13. [7] Z. Shen, Riemann-Finsler geometry with applications to information geometry, Chin. Ann. Math. 27(2006), 73-94. [8] Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, 2001. [9] Z. Shen, Volume comparison and its applications in Riemann-Finsler geometry, Adv. Math. 128(1997), 306-328. [10] Z. Shen, On R-quadratic Finsler spaces, Publ. Math. Debrecen. 58(2001), 263-274. [11] A. Tayebi and M. Barzegari, Generalized Berwald spaces with (α, β)-metrics, Indagationes. Math. (N.S.). 27(2016), 670-683. [12] A. Tayebi and F. Eslami, On a class of generalized Berwald manifolds, Publ. Math. Debrecen, 105(2024), 379-402. [13] A. Tayebi and B. Najafi, Shen’s processes on Finslerian connection theorey, Bull. Iran. Math. Soc. 36(2010), 2198-2204. [14] A. Tayebi and M. Rafie. Rad, S-curvature of isotropic Berwald metrics, Sci. China. Series A: Math. 51(2008), 2198-2204. [15] C. Vincze, On a special type of generalized Berwald manifolds: semi-symmetric linear connections preserving the Finslerian length of tangent vectors, European Journal of Math. 3(2017), 1098-1171. [16] C. Vincze, On generalized Berwald manifolds with semi-symmetric compatible linear connections, Publ. Math. Debrecen. 83(2013), 741-755. [17] M. Zohrehvand, On the existence of 3-dimensional Berwald manifolds, J. Finsler Geom. Appl. 2(1) (2021), 86-95. | ||
|
آمار تعداد مشاهده مقاله: 1 تعداد دریافت فایل اصل مقاله: 3 |
||