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Hedayatian, Sina, Izadian, Neda, Yar Ahmadi, Mohammad. (1400). A class of Finsler metrics with bounded non-Riemannian curvatures. سامانه مدیریت نشریات علمی, 2(1), 40-50. doi: 10.22098/jfga.2021.1262
Sina Hedayatian; Neda Izadian; Mohammad Yar Ahmadi. "A class of Finsler metrics with bounded non-Riemannian curvatures". سامانه مدیریت نشریات علمی, 2, 1, 1400, 40-50. doi: 10.22098/jfga.2021.1262
Hedayatian, Sina, Izadian, Neda, Yar Ahmadi, Mohammad. (1400). 'A class of Finsler metrics with bounded non-Riemannian curvatures', سامانه مدیریت نشریات علمی, 2(1), pp. 40-50. doi: 10.22098/jfga.2021.1262
Hedayatian, Sina, Izadian, Neda, Yar Ahmadi, Mohammad. A class of Finsler metrics with bounded non-Riemannian curvatures. سامانه مدیریت نشریات علمی, 1400; 2(1): 40-50. doi: 10.22098/jfga.2021.1262

A class of Finsler metrics with bounded non-Riemannian curvatures

Journal of Finsler Geometry and its Applications
مقاله 3، دوره 2، شماره 1، مهر 2021، صفحه 40-50    اصل مقاله (100.94 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2021.1262
نویسندگان
Sina Hedayatian* 1؛ Neda Izadian2؛ Mohammad Yar Ahmadi3
1Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz-Iran. Email: hedayatian@scu.ac.ir
2Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz-Iran. Email: nezadiyan@gmail.com
3Department of Mathematics, Faculty of Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz-Iran. Email: m.yarahmadi@scu.ac.ir
چکیده
In this paper, we find a necessary and sufficient condition for a class of Finsler metrics defined by a Riemannian metric and a 1-form on a manifold which has bounded mean Cartan torsion. Moreover, we obtain a necessary and sufficient condition under which the above mentioned class of Finsler metrics has bounded mean Landsberg curvature. Next, we investigate these metrics with bounded mean Cartan torsion and mean Landsberg curvature. Furthermore, we give explicit examples of this type of metrics.
کلیدواژه‌ها
(α؛ β)-metric؛ Cartan torsion؛ mean Cartan torsion؛ Landsberg curvature؛ mean Landsberg curvature
مراجع
  • 1. S. B´acs´o, X. Cheng, and Z. Shen, Curvature properties of (α, β)-metrics, Adv. Stud.
    Pure. Math. Soc. Japan. 48(2007), 73-110.
  • 2. D. Bao and S. S. Chern, A note on the Gauss-Bonnet theorem for Finsler spaces, Ann.
    Math. 143(1996), 233252.
  • 3. D. Bao and Z. Shen, Finsler metrics of constant positive curvature on the Lie group S
    3,J. London. Math. Soc. 66(2002), 453-467.
  • 4. D. Burago and S. Ivanov, Isometric embedding of Finsler manifolds, Algebra i Analiz,
    5(1993), 179-192.
  • 5. E. Cartan, Les spaces de Finsler. Actualites Scientifiques et industrilles, no. 79, Hermann,
    Paris, 1934.
  • 6. X. Cheng and Z. Shen, A class of Finsler metrics with isotropic S-curvature, Israel J.
    Math. 169(2009), 317-340.
  • 7. X. Cheng, Z. Shen and Y. Tian, A class of Einstein (α, β)-metrics, Israel J. Math,
    192(2012), 221-249.
  • 8. X. Cheng, H. Wang and M. Wang, (α, β)-metrics with relatively isotropic mean Landsberg
    curvature, Publ. Math. Debrecen, 72(2008), 475-485.
  • 9. S.S. Chern and Z. Shen, Riemann-Finsler Geometry, World Scientific, Singapore, 2005.
  • 10. P. Finsler, Uber Kurven und Fl¨achen in allgemeinen R¨aumen ¨ . Verlag Birkh¨auser, Basel,
    1951.
  • 11. R. S. Ingarden, Uber die Einbetting eines Finslerschen Rammes in einan Minkowskischen ¨
    Raum, Bull. Acad. Polon. Sci. III, 2(1954), 305-308.
  • 12. B. Li and Z. Shen, On a class of weak Landsberg metrics, Science in China Series A.
    50(2007),75-85.
  • 13. X. Mo and L. Zhou, A class of Finsler metrics with bounded Cartan torsion, Canad.
    Math. Bull. 53(2010), 122-132.
  • 14. J. Nash, The imbedding problem for Riemannian manifolds, Ann. Math. 73(1957), 20-37.
  • 15. T. Rajabi, On the norm of Cartan torsion of two classes of (α, β)-metrics, Journal of
    Finsler Geometry and its Applications, 1(1) (2020), 66-72.
  • 16. Z. Shen, On a class of Landsberg metrics in Finsler geometry, Canadian. J. Math.
    61(2009), 1357-1374.
  • 17. Z. Shen, On Finsler geometry of submanifolds, Math. Ann. 311(1998), 549-576.
  • 18. Z. Shen, On R-quadratic Finsler spaces, Publ. Math. Debrecen, 58(2001), 263-274.
  • 19. Z. Shen, Differential Geometry of Spray and Finsler Spaces, Kluwer Academic Publishers, 2001.
  • 20. A. Tayebi and H. Sadeghi, On Cartan torsion of Finsler metrics, Publ. Math. Debrecen,
    82(2013), 461-471.
  • 21. G. Yang, On a class of singular Douglas and projectively flat Finsler metrics, Differ.
    Geom. Appl. 32(2014), 113-129.
  • 22. G. Yang, On a class of singular projectively flat Finsler metrics with constant flag curvature, Int. J. Math. 24(2013), 16 pages, 1350087.
  • 23. L. Zhou, A local classification of a class of (α, β)-metrics with constant flag curvature.
    Differ. Geom. Appl. 28(2010), 170-193
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