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Kumar, Sachin, Singh, Abhishek, Dwivedi, P. K., Mishra, C. K., Shanker, Uma. (1404). Study of some curvatures with Z. Shen's square metric. سامانه مدیریت نشریات علمی, 6(2), 41-52. doi: 10.22098/jfga.2025.17260.1157
Sachin Kumar; Abhishek Singh; P. K. Dwivedi; C. K. Mishra; Uma Shanker. "Study of some curvatures with Z. Shen's square metric". سامانه مدیریت نشریات علمی, 6, 2, 1404, 41-52. doi: 10.22098/jfga.2025.17260.1157
Kumar, Sachin, Singh, Abhishek, Dwivedi, P. K., Mishra, C. K., Shanker, Uma. (1404). 'Study of some curvatures with Z. Shen's square metric', سامانه مدیریت نشریات علمی, 6(2), pp. 41-52. doi: 10.22098/jfga.2025.17260.1157
Kumar, Sachin, Singh, Abhishek, Dwivedi, P. K., Mishra, C. K., Shanker, Uma. Study of some curvatures with Z. Shen's square metric. سامانه مدیریت نشریات علمی, 1404; 6(2): 41-52. doi: 10.22098/jfga.2025.17260.1157

Study of some curvatures with Z. Shen's square metric

Journal of Finsler Geometry and its Applications
دوره 6، شماره 2، 2025، صفحه 41-52    اصل مقاله (292.14 K)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22098/jfga.2025.17260.1157
نویسندگان
Sachin Kumar* 1؛ Abhishek Singh2؛ P. K. Dwivedi2؛ C. K. Mishra2؛ Uma Shanker2
1Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya(U. P.), India
2Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya(U.P.), India
چکیده
In this research paper, we have studied the Z-Shen square metric under the condition that the 1-form β is a Killing form of constant length. We have derived the explicit expressions for the Ricci and Riemann curvatures associated with this metric. Furthermore, we have investigated the special characteristics of projectively flat Z-Shen square metrics that possess isotropic S-curvature
کلیدواژه‌ها
Z-Shen's square metric؛ Projectively flat Finsler space؛ S-curvature؛ Ricci curvature؛ Riemann curvature
مراجع
 1. S.S. Chern and Z. Shen, Riemann- Finsler Geometry, World Scientific, Singapore, (2005).
2. V. K. Kropina, On Projective Two dimensional Finsler spaces with special metric ,Trudy Sem. Vector Tenzor Anal. 11(1961), 277-292.
3. M. Matsumoto, Foundation of Finsler geometry and special Finsler spaces, Kaiseisha Press, Saikawa, Otsu, 520, Japan, 1986
4. Z. Shen, Volume comparision and its applications in Riemann-Finsler geometry, Adv.Math. 128(1997), 306-328.
5. Z. Shen , Lectures on Finsler Geometry, World Scientific, Singapore, (2001).
6. Z. Shen, Finsler metrics with K = 0 an S = 0, Can. J. Math. 55(1) (2003), 112-132.
7. X. Zhang and Y. B. Shen, On Einstein Kropina Metrics, arXiv:1207.1944v1[math.DG](2012).
8. Amr Soleiman and Salah Gomaa Elgendi, On Generalized Shen’s Square metric, Korean J. Math. 32(3) (2024), 467-484.
9. P. K. Dwivedi, C.K. Mishra and Sachin Kumar, On Projectively-flat Finsler space with n-power (α; β)-metric, J. Finsler Geom. Appl. 5(2) (2024), 14-24.
10. H. G. Nagaraja, On Kropina metrics , J. African. Math. Union, (2013) 

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