Open Access
January 2019 On the theory of $4$-th root Finsler metrics
Akbar Tayebi
Tbilisi Math. J. 12(1): 83-92 (January 2019). DOI: 10.32513/tbilisi/1553565628


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.


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Akbar Tayebi. "On the theory of $4$-th root Finsler metrics." Tbilisi Math. J. 12 (1) 83 - 92, January 2019.


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

zbMATH: 07172302
MathSciNet: MR3954221
Digital Object Identifier: 10.32513/tbilisi/1553565628

Primary: 53B40
Secondary: 53C60

Keywords: $4$-th root metric , locally dually flat metric , projectively flat metric

Rights: Copyright © 2019 Tbilisi Centre for Mathematical Sciences

Vol.12 • No. 1 • January 2019
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