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Study of some curvatures with Z. Shen's square metric | ||
Journal of Finsler Geometry and its Applications | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 خرداد 1404 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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