In this paper, we study reversibility of Riemann Curvature and Ricci curvature for the Ingarden-Támassy metric and prove two global results. First, we prove that a Ingarden-Támassy metric is R-reversible if and only if si = 0, sij|k = 0. Then we show that a Ingarden-Támassy metric is Ricci-reversible if and only if si = 0.
1. S. B´acs´o, X. Cheng and Z. Shen, Curvature properties of (α, β)-metrics, Advanced Studies in Pure Mathematics, Math. Soc. Japan. 48(2007), 73–110.
2. M. Crampin, Randers spaces with reversible geodesics, Publ. Math. Debrecen. 67(34) (2005), 401–409.
3. S. S. Chern and Z. Shen, Riemann-Finsler Geometry, World Scientific, Singapore, (2005).
4. X. Cheng, Z. Shen and Y. Tian, A class of Einstein (α, β)-metrics, Israel J. Math. 192(1)(2012), 221–249.
5. R. S. Ingarden and L. T´amassy, The point Finsler spaces and their physical applications in electron optics and thermodynamics, Math. Comput. Modelling, 20(1994), 93–107.
6. B. Li and Z. Shen, On Randers metrics of quadratic Riemann curvature, Intern. J. Math. 20(2009), 1–8.
7. I.M. Masca, S.V. Sabau and H. Shimada, Reversible geodesics for (α, β)-metrics, International. J. Math. 21(8) (2010), 1071–1094.
8. I.M. Masca, S.V. Sabau and H. Shimada, Necessary and sufficient conditions for two dimensional (α, β)-metrics with reversible geodesics, preprint.
9. M. Matsumoto, A slope of a hill is a Finsler surface with respect to a time measure, J. Math. Kyoto. Univ. 29(1980), 17–25.
10. Z. Shen and G. Yang, Randers metrics of reversible curvature, Intern. J. Math. 24(1) (2013), 1350006 (16 pages).
11. H. Shimada and S.V. Sabau, An introduction to Matsumoto metric, Nonlinear Analysis: RWA. 63(2005) 165–168.
12. A. Tayebi, E. Peyghan and H. Sadeghi, On Matsumoto-type Finsler metrics, Nonlinear Analysis: RWA, 13(2012), 2556–2561.
13. A. Tayebi, T. Tabatabaeifar and E. Peyghan, On the second approximate Matsumoto metric, Bull. Korean Math. Soc. 51(1) (2014), 115–128.
14. A. Tayebi and T. Tabatabaeifar, Matsumoto metric of reversible curvatures, Acta. Math. Acad. Paedagogicae Nyiregyhaziensis, 32(2016), 165–200.
15. B. Tiwari, G.K. Prajapati and R. Gangopadhyay, On Finsler spaces with rational spray coefficiients, Differ. Geom. 21(2019), 180–188.
Izadian, N. (2023). On Riemannian and Ricci curvatures of Ingarden-Támassy metrics. Journal of Finsler Geometry and its Applications, 4(2), 128-150. doi: 10.22098/jfga.2023.14082.1108
MLA
Neda Izadian. "On Riemannian and Ricci curvatures of Ingarden-Támassy metrics", Journal of Finsler Geometry and its Applications, 4, 2, 2023, 128-150. doi: 10.22098/jfga.2023.14082.1108
HARVARD
Izadian, N. (2023). 'On Riemannian and Ricci curvatures of Ingarden-Támassy metrics', Journal of Finsler Geometry and its Applications, 4(2), pp. 128-150. doi: 10.22098/jfga.2023.14082.1108
VANCOUVER
Izadian, N. On Riemannian and Ricci curvatures of Ingarden-Támassy metrics. Journal of Finsler Geometry and its Applications, 2023; 4(2): 128-150. doi: 10.22098/jfga.2023.14082.1108