In this paper, we first study a special class of (α,β)-metrics in the form F = α + εβ + k β2/α , where α is Riemannian metric, β is a 1-form, and ε,k(≠ 0) are constant. We give a complete classification for such metrics to be locally dually flat. By assumption β is a conformal 1-form, we show that the metric is locally dually flat if and only if α is a Euclidean metric and β is a constant 1-form. Further, we classify locally dually flat of a class of Finsler metric in the form F = α exp( α/β ) + εβ, where ε is constant.
Masoumi, S., Rezaei, B., & Gabrani, M. (2022). On a special class of dually flat (α, β)-metrics. Journal of Finsler Geometry and its Applications, 3(1), 141-154. doi: 10.22098/jfga.2022.10850.1066
MLA
Saeedeh Masoumi; Bahman Rezaei; Mehran Gabrani. "On a special class of dually flat (α, β)-metrics". Journal of Finsler Geometry and its Applications, 3, 1, 2022, 141-154. doi: 10.22098/jfga.2022.10850.1066
HARVARD
Masoumi, S., Rezaei, B., Gabrani, M. (2022). 'On a special class of dually flat (α, β)-metrics', Journal of Finsler Geometry and its Applications, 3(1), pp. 141-154. doi: 10.22098/jfga.2022.10850.1066
VANCOUVER
Masoumi, S., Rezaei, B., Gabrani, M. On a special class of dually flat (α, β)-metrics. Journal of Finsler Geometry and its Applications, 2022; 3(1): 141-154. doi: 10.22098/jfga.2022.10850.1066
)