The Deformation of an $(\alpha, \beta)$-Metric

Abstract

In this paper, we will continue our investigation on the new recently introduced $(\alpha, \beta)$-metric $F=\beta+\frac{a\alpha^{2}+\beta^{2}}{\alpha}$ in \cite{Pis}; where $\alpha$ is a Riemannian metric; $\beta$ is a 1-form, and $a\in \left(\frac{1}{4},+\infty\right)$ is a real positive scalar. We will investigate the deformation of this metric, and we will investigate its properties.

Keywords

• Finsler metric
• Finsler $(\alpha, \beta)$-metric
• deformation of an $(\alpha, \beta)$-metric

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References

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