Abstract
In this paper, we consider exponential change of Finsler metrics. First, we find a condition under which the exponential change of a Finsler metric is projectively related to it. Then we restrict our attention to the $4$-th root metric. Let $F=\sqrt[4]{A}$ be an $4$-th root Finsler metric on an open subset $U\subset \mathbb{R}^n$ and ${\bar F}=e^{\beta/F}F$ be the exponential change of $F$. We show that ${\bar F}$ is locally projectively flat if and only if it is locally Minkowskian. Finally, we obtain necessary and sufficient condition under which ${\bar F}$ be locally dually flat.
Acknowledgment
The author would like to thank the anonymous referees for their suggestions and comments which helped in improving the paper.
Citation
Akbar Tayebi. "On the theory of $4$-th root Finsler metrics." Tbilisi Math. J. 12 (1) 83 - 92, January 2019. https://doi.org/10.32513/tbilisi/1553565628
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