Tbilisi Mathematical Journal

On the theory of $4$-th root Finsler metrics

Akbar Tayebi

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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.


The author would like to thank the anonymous referees for their suggestions and comments which helped in improving the paper.

Article information

Tbilisi Math. J., Volume 12, Issue 1 (2019), 83-92.

Received: 27 April 2018
Accepted: 20 December 2018
First available in Project Euclid: 26 March 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 53B40: Finsler spaces and generalizations (areal metrics)
Secondary: 53C60: Finsler spaces and generalizations (areal metrics) [See also 58B20]

locally dually flat metric projectively flat metric $4$-th root metric


Tayebi, Akbar. On the theory of $4$-th root Finsler metrics. Tbilisi Math. J. 12 (2019), no. 1, 83--92. doi:10.32513/tbilisi/1553565628. https://projecteuclid.org/euclid.tbilisi/1553565628

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