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

Articles in Press

Document Type : Original Article

Authors

1 Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya(U. P.), India

2 Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya(U.P.), India

10.22098/jfga.2025.17260.1157

Abstract

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

Keywords

References

 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) 
Journal of Finsler Geometry and its Applications

Articles in Press, Accepted Manuscript
Available Online from 02 June 2025

Files

Share

How to cite

Statistics