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In this paper, we characterize the conformal transformations between two almost regular $(\alpha,\beta)$-metrics. Suppose that $F$ is a non-Riemannian $(\alpha,\beta)$-metric and is conformally related to $\tF$, that is, $\tilde{F}=e^{\kappa(x)}F$, where $\kappa:=\kappa(x)$ is a scalar function on the manifold. We obtain the necessary and sufficient conditions of the conformal transformation between $F$ and $\tF$ preserving the mean Landsberg curvature. Further, when both $F$ and $\tF$ are regular, the conformal transformation between $F$ and $\tF$ preserving the mean Landsberg curvature must be a homothety.
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참고문헌 (17)
참고문헌 신청
S. Bacso / 2007 / Finsler conformal transformations and the curvature invariances / Publ. Math. Debrecen 70(1-2):221~231
S. Bacso / 2007 / Curvature properties of (${\alpha}$ , ${\beta}$ )-metrics, in Finsler geometry, Sapporo 2005-in memory of Makoto Matsumoto, Adv. Stud. Pure Math., 48 :73~110
G. Chen / 2013 / An important class of conformally flat weak Einstein Finsler metrics / Internat. J. Math. 24(1):15
G. Chen / 2013 / On conformal transformations between two (${\alpha}$ , ${\beta}$ )- metrics / Differential Geom. Appl. 31(2):300~307
G. Chen / 2015 / On conformally flat (${\alpha}$ , ${\beta}$ )-metrics with constant flag curvature / Publ. Math. Debrecen 86(3-4):387~400
S. Bacso / 2007 / Curvature properties of (
G. Chen / 2013 / An important class of conformally flat weak Einstein Finsler metrics / Internat. J. Math. 24(1):15
G. Chen / 2013 / On conformal transformations between two (
G. Chen / 2015 / On conformally flat (
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