On general $(\alpha,\beta)$-metrics with Cartan torsion, mean Cartan torsion and Landsberg curvature

Kumar, Manoj; Mishra, Chayan Kumar; Singh, Abhishek; Singh, Achal

doi:10.22060/ajmc.2022.21094.1077

دانشگاه صنعتی امیرکبیر

تعداد نشریات	7
تعداد شماره‌ها	399
تعداد مقالات	5,389
تعداد مشاهده مقاله	5,288,038
تعداد دریافت فایل اصل مقاله	4,882,776

	On general $(\alpha,\beta)$-metrics with Cartan torsion, mean Cartan torsion and Landsberg curvature
AUT Journal of Mathematics and Computing
مقاله 1، دوره 4، شماره 2، 2023، صفحه 105-112 اصل مقاله (365.94 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2022.21094.1077
نویسندگان
Manoj Kumar^* ¹؛ Chayan Kumar Mishra¹؛ Abhishek Singh¹؛ Achal Singh²
¹Department of Mathematics and Statistics Faculty of Science, Dr. Rammanohar Lohia Avadh University, Ayodhya-224001, India
²Department of Mathematics Institute of Applied Sciences and Humanities GLA University Mathura-281406, India
چکیده
In this paper, we derive a formula for the (mean) Cartan torsion of a class of general $(\alpha,\beta)$-metrics. Also, we study weak Landsberg general $(\alpha,\beta)$-metrics under a certain condition.
کلیدواژه‌ها
Finsler space؛ Cartan torsion؛ Landsberg curvature؛ Mean Cartan torsion؛ Weak Landsberg curvature

مراجع
[1] A. Ala, A. Behzadi, and M. Rafiei-Rad, On general (α, β)-metrics of weak Landsberg type, 2017. preprint. [2] R. Bryant, Finsler structures on the 2-sphere satisfying K = 1, in Finsler Geometry (Seattle, WA, 1995), vol. 196, Amer. Math. Soc., Providence, RI, 1996, pp. 27–41. [3] , Projectively flat finsler 2-spheres of constant curvature, Sel. math. (New ser.), 3 (1997), pp. 161–203. [4] S.-S. Chern, Finsler geometry is just Riemannian geometry without the quadratic restriction, Notices Amer. Math. Soc., 43 (1996), pp. 959–963. [5] S.-S. Chern and Z. Shen, Riemann-Finsler geometry, vol. 6 of Nankai Tracts in Mathematics, World Sci[1]entific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005. [6] M. Matsumoto, On C-reducible Finsler spaces, Tensor (N.S.), 24 (1972), pp. 29–37. [7] G. Randers, On an asymmetrical metric in the fourspace of general relativity, Phys. Rev. (2), 59 (1941), pp. 195–199. [8] S. F. Rutz, Symmetry in Finsler spaces, in Finsler geometry (Seattle, WA, 1995), vol. 196 of Contemp. Math., Amer. Math. Soc., Providence, RI, 1996, pp. 289–300. [9] E. S. Sevim, Z. Shen, and S. Ulgen ¨ , Spherically symmetric Finsler metrics with constant Ricci and flag curvature, Publ. Math. Debrecen, 87 (2015), pp. 463–472. [10] Z. Shen, Differential geometry of spray and Finsler spaces, Kluwer Academic Publishers, Dordrecht, 2001. [11] A. Tayebi, E. Peyghan, and H. Sadeghi, On locally dually flat (α, β)-metrics with isotropic S-curvature, Indian J. Pure Appl. Math., 43 (2012), pp. 521–534. [12] A. Tayebi, H. Sadeghi, and E. Peyghan, On a class of locally dually flat (α, β)-metrics, Math. Slovaca, 65 (2015), pp. 191–198. [13] C. Yu and H. Zhu, On a new class of Finsler metrics, Differential Geom. Appl., 29 (2011), pp. 244–254. [14] , Projectively flat general (α, β)-metrics with constant flag curvature, J. Math. Anal. Appl., 429 (2015), pp. 1222–1239. [15] L. Zhou, Spherically symmetric Finsler metrics in Rn, Publ. Math. Debrecen, 80 (2012), pp. 67–77. [16] , The spherically symmetric Finsler metrics with isotropic S-curvature, J. Math. Anal. Appl., 431 (2015), pp. 1008–1021. [17] M. Zohrehvand and H. Maleki, On general (α, β)-metrics of Landsberg type, Int. J. Geom. Methods Mod. Phys., 13 (2016), pp. 1650085, 13.
آمار تعداد مشاهده مقاله: 1,173 تعداد دریافت فایل اصل مقاله: 835

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

آمار

On general $(\alpha,\beta)$-metrics with Cartan torsion, mean Cartan torsion and Landsberg curvature