Conformal ‎T‎ransformation of ‎L‎ocally ‎D‎ually ‎F‎lat‎‎‎ Finsler ‎metrics
Bull. Korean Math. Soc.
Published online 2018 Sep 21
‎Laya ‎Ghasemnezhad, and Bahman Rezaei
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 ‎\textbf{C}-reducible ‎metrics‎ must be ‎homothetic‎‎‎.
Keywords : Conformal ‎Transformation, ‎Locally ‎dually ‎flat, ‎Randers ‎mtric, ‎Kropina ‎metric
MSC numbers : 53C60
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