Tbilisi Mathematical Journal

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

Akbar Tayebi

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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.

Note

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1553565628

Digital Object Identifier
doi:10.32513/tbilisi/1553565628

Mathematical Reviews number (MathSciNet)
MR3954221

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

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

Citation

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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