پیوندهای مفید
آمار
| تعداد نشریات | 30 |
| تعداد شماره‌ها | 414 |
| تعداد مقالات | 3,651 |
| تعداد مشاهده مقاله | 5,762,405 |
| تعداد دریافت فایل اصل مقاله | 3,942,001 |
On Cartan torsion of 4-dimensional Finsler manifolds | ||
| Journal of Hyperstructures | ||
| دوره 13، شماره 1، 2024، صفحه 134-141 اصل مقاله (280.68 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2024.15204.1019 | ||
| نویسنده | ||
| Akbar Tayebi* | ||
| Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran | ||
| چکیده | ||
| There are several non-Riemannian curvatures in Finsler geometry which show the complexity of Finsler geometry with respect to Riemannian geometry. Amon these quantities, the Cartan and mean Cartan torsion have very important and brilliant positions. In this paper, we find the necessary and sufficient condition under which a 4-dimensional Finsler manifold is C-reducible. Also, we find the necessary and sufficient condition under which a 4-dimensional Finsler manifold has vanishing ${\bar I}$-curvature. | ||
| کلیدواژه‌ها | ||
| Cartan torsion؛ mean Cartan torsion؛ C-reducible metric | ||
| مراجع | ||
|
[1] D. Burago and S. Ivanov, Isometric embedding of Finsler manifolds, Algebra. Analiz., 5 (1993), 179-192. [2] E. Cartan, Les espaces de Finsler, Actualities 79, Paris, 1934. [3] X. Cheng and Z. Shen, Finsler Geometry- An Approach via Randers Spaces, Springer, Heidelberg and Science Press, Beijing, 2012. [4] A. Deicke, Uber die Finsler-Raume mit Ai = 0, Arch. Math., 4(1953), 45-51. [5] P. Finsler, Uber Kurven und Flachen in allgemeinen Raumen, (Dissertation, Gottingan, 1918), Birkhauser Verlag, Basel, 1951. [6] R. S. Ingarden, Uber die Einbetting eines Finslerschen Rammes in einan Minkowskischen Raum, Bull. Acad. Polon. Sci., 2(1954), 305-308. [7] M. Matsumoto, Theory of Finsler spaces with (α; β)-metric, Rep. Math. Phys., 31(1992), 43-84. [8] M. Matsumoto and S. Hojo, A conclusive theorem for C-reducible Finsler spaces, Tensor. N. S. ,32(1978), 225-230. [9] X. Mo and L. Zhou, A class of Finsler metrics with bounded Cartan torsion, Canad. Math. Bull. , 53(2010), 122-132. [10] B. N. Prasad and G. Shanker, Conformal change of four-dimensional Finsler space, Bull. Cal. Math. Soc., 102(5) (2010), 423-432. [11] T. Rajabi, On the norm of Cartan torsion of two classes of (α; β)-metrics, J. Finsler Geom. Appl., 1(1) (2020), 66-72. [12] H. Sadeghi, Finsler metrics with bounded Cartan torsion, J. Finsler Geom. Appl., 2(1) (2021), 51-62. [13] Z. Shen, On Finsler geometry of submanifolds, Math. Annal., 311(1998), 549-576. [14] Z. Shen, On R-quadratic Finsler spaces, Publ. Math. Debrecen, 58(2001), 263-274. [15] Z. Shen, Di erential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, 2001. [16] A. Tayebi and H. Sadeghi, On Cartan torsion of Finsler metrics, Publ. Math. Debrecen., 82(2) (2013), 461-471. | ||
|
آمار تعداد مشاهده مقاله: 171 تعداد دریافت فایل اصل مقاله: 190 |
||