University of Mohaghegh ArdabiliJournal of Finsler Geometry and its Applications2783-05003120220701On a special class of dually flat (α, β)-metrics141154173810.22098/jfga.2022.10850.1066ENSaeedeh MasoumiDepartment of Mathematics, Faculty of Science, Urmia University
Urmia, Iran.Bahman RezaeiDepartment of Mathematics, Faculty of Science, Urmia University
Urmia, Iran.Mehran GabraniDepartment of Mathematics, Faculty of Science, Urmia University
Urmia, Iran.Journal Article20220523In this paper, we first study a special class of (α,β)-metrics in the form F = α + εβ + k β<sup>2</sup>/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.https://jfga.uma.ac.ir/article_1738_37921fee9fc164d785ddb369281fe62d.pdf