آمار

تعداد نشریات30
تعداد شماره‌ها434
تعداد مقالات3,803
تعداد مشاهده مقاله6,096,603
تعداد دریافت فایل اصل مقاله4,178,905
Masoumi, Saeedeh, Rezaei, Bahman, Gabrani, Mehran. (1401). On a special class of dually flat (α, β)-metrics. سامانه مدیریت نشریات علمی, 3(1), 141-154. doi: 10.22098/jfga.2022.10850.1066
Saeedeh Masoumi; Bahman Rezaei; Mehran Gabrani. "On a special class of dually flat (α, β)-metrics". سامانه مدیریت نشریات علمی, 3, 1, 1401, 141-154. doi: 10.22098/jfga.2022.10850.1066
Masoumi, Saeedeh, Rezaei, Bahman, Gabrani, Mehran. (1401). 'On a special class of dually flat (α, β)-metrics', سامانه مدیریت نشریات علمی, 3(1), pp. 141-154. doi: 10.22098/jfga.2022.10850.1066
Masoumi, Saeedeh, Rezaei, Bahman, Gabrani, Mehran. On a special class of dually flat (α, β)-metrics. سامانه مدیریت نشریات علمی, 1401; 3(1): 141-154. doi: 10.22098/jfga.2022.10850.1066

On a special class of dually flat (α, β)-metrics

Journal of Finsler Geometry and its Applications
مقاله 12، دوره 3، شماره 1، مهر 2022، صفحه 141-154    اصل مقاله (94.13 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2022.10850.1066
نویسندگان
Saeedeh Masoumi؛ Bahman Rezaei* ؛ Mehran Gabrani
Department of Mathematics, Faculty of Science, Urmia University Urmia, Iran.
چکیده
In this paper, we first study a special class of (α,β)-metrics in the form F = α + εβ + k β2/α , where α is Riemannian metric, β is a 1-form, and ε,k(≠ 0) are constant. We give a complete classification for such metrics to be locally dually flat. By assumption β is a conformal 1-form, we show that the metric is locally dually flat if and only if α is a Euclidean metric and β is a constant 1-form. Further, we classify locally dually flat of a class of Finsler metric in the form F = α exp( α/β ) + εβ, where ε is constant.
کلیدواژه‌ها
Finsler metric؛ (α؛ β)- metric؛ locally dually flat
مراجع
  • 1. S.-I. Amari and H. Nagaoka, Methods of information geometry, AMS Translation of
    Math. Monographs 191, Oxford University Press, 2000.
  • 2. S. Bcs, X. Cheng, and Z. Shen, Curvature properties of (α, β)-metrics. In Finsler Geometry, Sapporo 2005In Memory of Makoto Matsumoto, Mathematical Society of Japan.
    (2007), 73–110.
  • 3. X. Cheng, Z. Shen, Finsler Geometry-An Approach via Randers spaces, Beijing: science
    press, (2012).
  • 4. X. Cheng, Z. Shen and Y. Zhou, On locally dually flat Randers metrics, Intern. Math.
    J. 21(11) 2010, 1531-1543.
  • 5. S. S. Chern, Z. Shen, Riemann-Finsler geometry, World Scientific Publishing Company.
    (Vol. 6) (2005).
  • 6. S.-S. Chern and Z. Shen, Riemann-Finsler geometry, Nankai Tracts in Mathematics,
    Vol. 6, World Scientific, (2005).
  • 7. Z. Shen, Riemann-Finsler geometry with applications to information geometry, Chinese
    Ann. Math. Ser. B. 27(1) (2006), 73-94.
  • 8. Bin Shen and Yanfang Tian, Rigidity theorems of some dually flat Finsler metrics and
    its applications. Bulletin of the Korean Mathematical Society 53, 5 (2016), 1457-1469.
  • 9. A. Tayebi, E. Peyghan, and H. Sadeghi, On locally dually flat (α, β)-metrics with
    isotropic S-curvature. Indian J. Pure Appl. Math. 43(5) (2012), 521-534.
  • 10. Q. Xia, On locally dually flat (α, β)-metrics, Differ. Geom. Appl. 29 (2011), 233-243.
  • 11. Q. Xia, On a class of locally dually flat Finsler metrics, Publ. Math. Debrecen. 78(1)
    (2011), 169-190. 
آمار
تعداد مشاهده مقاله: 229
تعداد دریافت فایل اصل مقاله: 308


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب