Conformal transformation of locally dually flat Finsler metrics
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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.
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.
참고문헌 (13)
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