Conformal transformation of locally dually flat Finsler metrics
Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 407-418
https://doi.org/10.4134/BKMS.b180288
Published online 2019 Mar 01
Laya Ghasemnezhad, Bahman Rezaei
Urmia University; Urmia University
Abstract : In this paper, we study conformal transformations between special class of Finsler metrics named $\textbf{C}$-reducible metrics. This class includes Randers metrics in the form $F=\alpha + \beta $ and Kropina metric in the form $F=\frac{\alpha^{2}}{\beta}$. We prove that every conformal transformation between locally dually flat Randers metrics must be homothetic and also every conformal transformation between locally dually flat Kropina metrics must be homothetic.
Keywords : conformal transformation, locally dually flat, Randers metric, Kropina metric, $\textbf{C}$-reducible metric
MSC numbers : 53C60, 53C25
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