آمار

تعداد نشریات27
تعداد شماره‌ها364
تعداد مقالات3,223
تعداد مشاهده مقاله4,741,220
تعداد دریافت فایل اصل مقاله3,238,574
Salimi Moghaddam, Hamid Reza, Abedi Karimi, Hossein, Nasehi, Mehri. (1399). Douglas (α,β)-metrics on four-dimensional nilpotent Lie groups. سامانه مدیریت نشریات علمی, 1(2), 15-26. doi: 10.22098/jfga.2020.1236
Hamid Reza Salimi Moghaddam; Hossein Abedi Karimi; Mehri Nasehi. "Douglas (α,β)-metrics on four-dimensional nilpotent Lie groups". سامانه مدیریت نشریات علمی, 1, 2, 1399, 15-26. doi: 10.22098/jfga.2020.1236
Salimi Moghaddam, Hamid Reza, Abedi Karimi, Hossein, Nasehi, Mehri. (1399). 'Douglas (α,β)-metrics on four-dimensional nilpotent Lie groups', سامانه مدیریت نشریات علمی, 1(2), pp. 15-26. doi: 10.22098/jfga.2020.1236
Salimi Moghaddam, Hamid Reza, Abedi Karimi, Hossein, Nasehi, Mehri. Douglas (α,β)-metrics on four-dimensional nilpotent Lie groups. سامانه مدیریت نشریات علمی, 1399; 1(2): 15-26. doi: 10.22098/jfga.2020.1236

Douglas (α,β)-metrics on four-dimensional nilpotent Lie groups

Journal of Finsler Geometry and its Applications
دوره 1، شماره 2، اسفند 2020، صفحه 15-26    اصل مقاله (100.08 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2020.1236
نویسندگان
Hamid Reza Salimi Moghaddam* 1؛ Hossein Abedi Karimi2؛ Mehri Nasehi3
1Department of Pure Mathematics, Faculty of Mathematics and Statistics, University of Isfahan, Isfahan, 81746-73441-Iran. Email: salimi.moghaddam@gmail.com
2Department of Mathematics, Isfahan University of Technology, Isfahan, 84156-83111-Iran. Email:hossein.abedikarimi@gmail.com
3Faculty of Basic Sciences, University of Shahreza, P. O. Box: 86149- 56841, Shahreza, Iran. Email: nasehi.mehri@gmail.com
چکیده
In this paper, we give a classification of left-invariant Douglas and Berwald (α,β)-metrics on simply connected four-dimensional nilpotent Lie groups. We show that there are not any bi-invariant Randers metrics on four-dimensional nilpotent Lie groups. Then, we explicitly give the flag curvature formulas and geodesic vectors of these spaces. Finally, we give the formula of S-curvature of left-invariant Randers metrics of Douglas type.
کلیدواژه‌ها
nilpotent Lie group؛ Riemannian metric؛ (α,β)-metric؛ flag curvature
مراجع
  • 1. H. An and S. Deng, Invariant (α, β)-metrics on homogeneous manifolds, Monatsh. Math.
    154(2008), 89-102.
  • 2. B. Aradi, Left invariant Finsler manifolds are generalized Berwald, Eur. J. Pure Appl.
    Math. 8(2015), 118-125.
  • 3. V.I. Arnold, Sur la ge´ome´trie diffe´rentielle des groupes de Lie de dimension infinie et
    ses applications a` l’hydrodynamique des fluides parfaits, Ann. Inst. Fourier (Grenoble)
    16 (1966), 319-361.
  • 4. M. Atashafrouz, Characterization of 3-dimensional left-invariant locally projectively flat
    Randers metrics, J. Finsler Geom. Appl. 1 (2020), 96-102.
  • 5. N. Boken, T. Sukilovic, S. Vukmirovic, Lorentz geometry of 4-dimensional nilpotent Lie
    groups, Geom. Dedicata 177 (2015), 83-102.
  • 6. S. S. Chern and Z. Shen, Riemann-Finsler geometry, World Scientific, Singapore, 2005.
  • 7. S. Deng, Homogeneous Finsler Spaces, Springer, New York, 2012.
  • 8. S. Deng, and Z. Hu, On flag curvature of homogeneous Randers spaces, Canad. J. Math.
    65(2013), 66-81.
  • 9. M. Hosseini, and H. R. Salimi Moghaddam, Classification of Douglas (α, β)-metrics on
    five dimensional nilpotent Lie groups, Int. J. Geom. Methods Mod. Phys. 17 no. 8(2020),
    2050112.
  • 10. O. Kowalski, L. Vanhecke, Riemannian manifolds with homogeneous geodesics, Boll.
    Unione Mat. Ital. 5 B(7)(1991), 189-246.
  • 11. S. Deng, M, Hosseini, H. Liu and H. R. Salimi Moghaddam, On the left invariant (α, β)-
    metrics on some Lie groups, Houston J. Math. 45 No. 4(2019), 1071-1088.
  • 12. F. Veroniquemand M. Ruzhansky, Quantization on nilpotent Lie Groups, Vol. 314. Cham,
    Switzerland: Birkhauser, 2016.
  • 13. D. Latifi, Bi-invariant Randers metrics on Lie groups, Publ. Math. Debrecen 76(2010),
    219-226.
  • 14. D. Latifi, Bi-invariant Finsler Metrics on Lie Groups, Australian J. Basic and Applied
    Sciences 5(12)(2011), 507-511.
  • 15. J. Lauret, Homogeneous nilmanifolds of dimension 3 and 4, Geom. Dedicata 68(1997),
    145-155.
  • 16. H. Liu and S. Deng, Homogeneous (α, β)-metrics of Douglas type, Forum Math. 27(2015),
    3149-3165.
  • 17. L. Magnin, Sur les alge`bres de Lie nilpotentes de dimension ≤ 7, J. Geom. Phys. 3(1)
    (1986), 119-144.
  • 18. Z. Shen, Volume comparison and its applications in Riemann-Finsler geometry, Adv.
    Math. 128(1997), 306-328.
  • 19. T. Sukilovic, Geometric properties of neutral signature metrics on 4-dimensional nilpotent Lie groups, Rev. Un. Mat. Argentina 57(2016), 23-47.
  • 20. T. Sukilovic, Isometry groups of 4-dimensional nilpotent Lie Groups, J. Math. Sci.
    225(4)(2017), 711-721.
  • 21. M. Parhizkar, H. R. Salimi Moghaddam, Geodesic Vector fields of invariant (α, β)-
    metrics on Homogeneous spaces, Int. Electron. J. Geom. 6(2)(2013), 39-44.
  • 22. C. Will, The space of solvsolitons in low dimensions, Ann. Global Anal. Geom.
    40(3)(2011), 291-309.
آمار
تعداد مشاهده مقاله: 330
تعداد دریافت فایل اصل مقاله: 321


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب