آمار

تعداد نشریات30
تعداد شماره‌ها414
تعداد مقالات3,654
تعداد مشاهده مقاله5,771,915
تعداد دریافت فایل اصل مقاله3,951,280
Alavi, Seiedeh Sedigheh. (1399). On the locally flat Finsler manifolds. سامانه مدیریت نشریات علمی, 1(2), 115-129. doi: 10.22098/jfga.2020.1245
Seiedeh Sedigheh Alavi. "On the locally flat Finsler manifolds". سامانه مدیریت نشریات علمی, 1, 2, 1399, 115-129. doi: 10.22098/jfga.2020.1245
Alavi, Seiedeh Sedigheh. (1399). 'On the locally flat Finsler manifolds', سامانه مدیریت نشریات علمی, 1(2), pp. 115-129. doi: 10.22098/jfga.2020.1245
Alavi, Seiedeh Sedigheh. On the locally flat Finsler manifolds. سامانه مدیریت نشریات علمی, 1399; 1(2): 115-129. doi: 10.22098/jfga.2020.1245

On the locally flat Finsler manifolds

Journal of Finsler Geometry and its Applications
دوره 1، شماره 2، اسفند 2020، صفحه 115-129    اصل مقاله (101.81 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2020.1245
نویسنده
Seiedeh Sedigheh Alavi*
Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. Email: sedighehalavi54@gmail.com
چکیده
It is proved that every locally flat Finsler manifold is a locally flat Riemannian manifold. Some low dimensional locally Finsler manifolds are classified. It is also proved that in a categorical sense, there is a correspondence between locally flat Finsler manifolds and locally hessian Riemannian manifolds
کلیدواژه‌ها
Locally flat manifolds؛ Finsler metric؛ Bieberbach groups؛ fourth root metric
مراجع
  • 1. L. Bieberbach, Uber die Bewegungsgruppen der Euklidischen R¨aume I ¨ , Math. Annalen,
    70(3) (1911), 297-336.
  • 2. L. Bieberbach, Uber die Bewegungsgruppen der Euklidischen R¨aume II: Die Gruppen ¨
    mit einem endlichen Fundamentalbereich, Math. Annalen, 72 (3) (1912), 400-412.
  • 3. X. Chen, X. Mo and Z. Shen, On the flag curvature of Finsler metrics of scalar curvature,
    J. London Math. Soc., 68(2003), 762-780.
  • 4. A. Deicke, Uber die Finsler-R¨aume mit ¨ Ai = 0, Arch. Math. 4 (1953), 45-51.
  • 5. S. Deng and Z. Hou, The Group of Isometries of a Finsler space, Pacific J. Math, 207(1),
    2002.
  • 6. N. Bogdan, The Mazur-Ulam theorem, arXiv: 1306.2380v1, (2013).
  • 7. A. Schoenflies, Kristallsysteme und Kristallstruktur, Teubner (1891).
  • 8. L. Charlap, Bieberbach Groups and Flat Manifolds, Springer, (1986).
  • 9. S. B. Myers and N. E. Steenrod, The Group of Isometries of a Riemannian Manifold,
    Annals of Math. Second Series, 40 (2) (1939), 400-416.
  • 10. Li. Chi-Kwong Norms, Isometries, and Isometry Groups, J. Amer. Math. Monthly.,
    107(4) (2000), 334-340.
  • 11. J. Fennel, Isometries between finite-dimensional normed vector spaces, Preprint, (2016).
  • 12. H. Shima, On certain locally flat homogeneous manifolds of solvable Lie groups, Osaka
    J. Math. 13 (1976), 213-229.
  • 13. H. Shima, Compact locally hessian manifolds, Osaka J. Math. 15 (1978), 509-513.
  • 14. A. Szczepa´nski, Geometry of crystallographic groups, Singapore, Singapor, World Scientific Publshing, (2012).
  • 15. Z, Shen, Differential Geometry of Spray and Finsler spaces, Kluwer Academic Publishers,
    2001.
  • 16. J. Wolf, Spaces of constant curvature, New York, MacGrow Hill, (1967).
  • 17. R.G. Torrom´e, Averaged structures associated to a Finsler structure,
    arXiv:math/0501058v9.
  • 18. H.C. Wang, On Finsler spaces with completly integrable equations of Killing, J. Lond.
    Math. Soc. 22 (1947), 5-9. 
آمار
تعداد مشاهده مقاله: 335
تعداد دریافت فایل اصل مقاله: 324


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب