پیوندهای مفید
آمار
| تعداد نشریات | 7 |
| تعداد شماره‌ها | 399 |
| تعداد مقالات | 5,389 |
| تعداد مشاهده مقاله | 5,288,027 |
| تعداد دریافت فایل اصل مقاله | 4,882,770 |
On GDW-Randers metrics on tangent Lie groups | ||
| AUT Journal of Mathematics and Computing | ||
| مقاله 4، دوره 2، شماره 1، اردیبهشت 2021، صفحه 27-36 اصل مقاله (344.63 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22060/ajmc.2020.18572.1038 | ||
| نویسندگان | ||
| Mona Atashafrouz1؛ Behzad Najafi* 1؛ Akbar Tayebi2 | ||
| 1Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran | ||
| 2Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran | ||
| چکیده | ||
| Let $G$ be a Lie group equipped with a left-invariant Randers metric $F$. Suppose that $F^v$ and $F^c$ denote the vertical and complete lift of $F$ on $TG$, respectively. We give the necessary and sufficient conditions under which $F^v$ and $F^c$ are generalized Douglas-Weyl metrics. Then, we characterize all 2-step nilpotent Lie groups $G$ such that their tangent Lie groups $(TG, F^c)$ are generalized Douglas-Weyl Randers metrics. | ||
| کلیدواژه‌ها | ||
| Left-invariant metric؛ Douglas metric؛ Generalized Douglas-Weyl Metrics؛ Randers metric | ||
| مراجع | ||
|
[1] F. Asgari and H. R. Salimi Moghaddam, Left invariant Randers metrics of Berwald type on tangent Lie groups, Int. J. Geom. Meth. Modern. Phys. 15(01) (2018), 1850015.
[2] F. Asgari and H. R. Salimi Moghaddam, Riemannian geometry of two families of tangent Lie groups, Bull. Iran. Math. Soc. 44 (2018), 193-203.
[3] M. Atshafrouz and B. Najafi, On Cheng-Shen conjecture in Finsler geometry, Int. J. Math (2020). https://doi.org/10.1142/S0129167X20500305.
[4] S. B´acs´o and M. Matsumoto, On Finsler spaces of Douglas type, A generalization of notion of Berwald space, Publ. Math. Debrecen. 51 (1997), 385-406.
[5] S. B´acs´o and I. Papp, A note on generalized Douglas space, Periodica. Math. Hung. 48 (2004), 181-184.
[6] J. Hilgert and K. H. Neeb, Structure and geometry of Lie groups, Springer Monographs in Mathematics, 2012.
[7] S. Homolya and O. Kowalski, Simply connected two-step homogeneous nilmanifolds of dimension 5, Note. Math. 26 (2006), 69-77.
[8] R. S. Ingarden, On the geometrically absolute optical representation in the electron microscope, Trav. Soc. Sci. Lett. Wrochlaw. Ser. B. 3 (1957), 60 pp.
[9] O. Kowalski and M. Sekizawa, Natural transformations of Riemannian metrics on manifolds to metrics on tangent bundles, Bull. Tokyo. Gakugei. Univ. Sect. IV. 40 (1988), 1-29.
[10] B. Najafi, Z. Shen and A. Tayebi, On a projective class of Finsler metrics, Publ. Math. Debrecen. 70 (2007), 211-219.
[11] B. Najafi and A. Tayebi, A new quantity in Finsler geometry, C. R. Acad. Sci. Paris. Ser. I. 349 (2011), 81-83.
[12] M. Nasehi, On 5-dimensional 2-step homogeneous Randers nilmanifolds of Douglas type, Bull. Iranian Math. Soc. 43 (2017), 695-706.
[13] DN. Pham, On the tangent Lie group of a symplectic Lie group, Riccerche di Mathematica. 68(2) (2019), 669-704.
[14] G. Randers, On an asymmetric metric in the four-space of general relativity, Phys. Rve. 59 (1941), 195-199.
[15] H.R. Salimi Moghaddam, On the Randers metrics on two-step homogeneous nilmanifolds of dimension five, Int. J. Geom. Meth. Mod. Phys. 8 (2011), 501-510.
[16] S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J. 10 (1958), 338-354. [17] A. Tayebi, H. Sadeghi and E. Peyghan, On generalized Douglas-Weyl spaces, Bull. Malays. Math. Sci. Soc. (2) 36(3) (2013), 587-594.
[18] A. Tayebi and H. Sadeghi, On generalized Douglas-Weyl (α, β)-metrics, Acta Mathematica Sinica, English Series. 31(10) (2015), 1611-1620.
[19] K. Yano and S. Kobayashi, Prolongations of tensor fields and connections to tangent bundles I, J. Math. Soc. Japan. 18(2) (1966), 194-210.
[20] K. Yano and S. Ishihara, Tangent and cotangent bundles, volume 16 of Pure and Applied Mathematics. Marcel Dekker, Inc., 1973. | ||
|
آمار تعداد مشاهده مقاله: 1,272 تعداد دریافت فایل اصل مقاله: 807 |
||