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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.
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참고문헌 (13)
참고문헌 신청
P. L. Antonelli / 1993 / The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology / Kluwer Academic Publishers Group
D. Bao / 2000 / An Introduction to Riemann-Finsler Geometry / Springer-Verlag
S. Basco / 2007 / Finsler conformal transformations and the curvature invari-ances / Publ. Math. Debrecen 70(1-2):221~231
G. Chen / 2013 / On conformal transformations between two (α,β)-metrics / Dierential Geom. Appl 31(2):300~307
G. Chen / 2016 / On dually at Kropina metrics / Internat. J. Math 27(12):13
D. Bao / 2000 / An Introduction to Riemann-Finsler Geometry / Springer-Verlag
S. Basco / 2007 / Finsler conformal transformations and the curvature invari-ances / Publ. Math. Debrecen 70(1-2):221~231
G. Chen / 2013 / On conformal transformations between two (α,β)-metrics / Dierential Geom. Appl 31(2):300~307
G. Chen / 2016 / On dually at Kropina metrics / Internat. J. Math 27(12):13
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