On the reversible geodesics of a Finsler space endowed with a special deformed $(\alpha, \beta)$-metric

Document Type : Original Article

Authors

1 Technical University of Cluj Napoca, North University Center of Baia Mare, Department of Mathematics and Computer Science, Victoriei 76, 430122 Baia Mare, Romania

2 "Vasile Alecsandri" National College, str. Vasile Alecsandri nr. 37, Bacau, Romania

3 Departamento de Matematica-ICE, Universidade Federal de Amazonas-UFAM, 69080-900 Manaus-AM, Brazil

4 Department of Mathematics, King Khalid University, 9004 Abha, Saudi Arabia

Abstract

The scope of this paper is twofold. On the one hand, we will investigate the reversible geodesics of a Finsler space endowed with the deformed newly introduced $(\alpha, \beta)$-metric
\begin{equation}
F_{\epsilon}(\alpha,\beta)=\frac{\beta^{2}+\alpha^{2}(a+1)}{\alpha}+\epsilon\beta
\end{equation}
where $\epsilon$ is a real parameter with $|\epsilon|<2\sqrt{a+1}$ and $a\in \left(\frac{1}{4},+\infty\right)$; and on the other hand, we will investigate the T-tensor for this metric.

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References

[1] M. Crampin, Randers spaces with reversible geodesics, Publ. Math. Debrecen, 67 (2005), 401-409.
[2] M. Crasmareanu, New tools in Finsler geometry: stretch and Ricci solitons, Math. Rep. (Bucur.) 16 (66)(1) (2014) 83-93.
[3] M. Crasmareanu, A gradient-type deformation of conics and a class of Finslerian flows, An. Stiint. Univ. Ovidius Constanta, Ser. Mat., 25 (2017), no. 2, 85-99.
[4] M. Crasmareanu, A complex approach to the gradient-type deformations of conics, Bull. Transilv. Univ. Brasov, Ser. III, Math. Inform. Phys., 10(59) (2) (2017) 59-62.
[5] S. Elgendi, L. Kozma, (α, β)-metrics satisfying the T-condition or the σT condition, The Journal of Geometric Analysis, http://doi.org/10.1007/s12220-020-00555-3, 2020.
[6] I. Masca, S. V. Sab˘au, H. Shimada, Reversible geodesics for (α, β)-metric, Int. J. Math., 21 (2010), 1071-1094.
[7] M. Matsumoto, On three dimensional Finsler spaces satisfying the T and Bp conditions, Tensor N.S., 29 (1975), 13-20.
[8] L. I. Pi¸scoran, V. N. Mishra, Projectivelly flatness of a new class of (α, β)-metrics, Georgian Mathematical Journal 26 (1) (2019) 133-139.
[9] L. I. Pi¸scoran, V. N. Mishra, S-curvature for a new class of (α, β)-metrics, RACSAM, doi:10.1007/s13398-016- 0358-3, 2017. [10] P. Laurian-Ioan, B. Najafi, C. Barbu, T. Tabatabaeifar, The deformation of an (α, β)-metrics, International Electronic Journal of Geometry, 2021, Accepted.
[11] S. V. Sab˘au, H. Shimada, Finsler manifolds with reversible geodesics, Rev. Roumaine Math. Pures Appl., 57, (2012), 91-103. 
[12] S. S. Chen, Z. Shen, Riemann-Finsler geometry, Singapore: World Scientific, 2005.
[13] A. Tayebi, H. Sadeghi, H. Peyghan, On Finsler metrics with vanishing S-curvature, Turkish J. Math., 38 (2014) 154-165.
AUT Journal of Mathematics and Computing
Volume 2, Issue 1
February 2021
Pages 73-80

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