Bulletin of the
Korean Mathematical Society BKMS

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