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

Volume 18, Issue 3, pp 381--387 Publication Date: August 26, 2018       Article History
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### Authors

Mohammad Rafee - Department of Mathematics, I. K. Gujral Punjab Technical University, Kapurthala, India. Avdhesh Kumar - Department of Mathematics, I. K. Gujral Punjab Technical University, Kapurthala, India. G. C. Chaubey - Department of Mathematics, T. D. P. G. College, V. B. S. Purvanchal University, Jaunpur, India.

### Abstract

This paper deals with the existence of reversible geodesics on a Finsler space with some $(\alpha,\beta)$-metrics. The conditions for a Finsler space $(M,F)$ to be with reversible geodesics are obtained. We study some geometrical properties of $F$ with reversible geodesics and prove that the Finsler metric $F$ induces a weighted quasi-metric $d_F$ on $M$.

### Keywords

• Reversible geodesics
• $(\alpha,\beta)$-metric
• distance
• quasi-metric
• weighted quasi-metric

•  53C60
•  53C22

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