University of Mohaghegh Ardabili Journal of Finsler Geometry and its Applications 2783-0500 1 2 2020 12 01 On the locally flat Finsler manifolds 115 129 1245 10.22098/jfga.2020.1245 EN Seiedeh Sedigheh Alavi Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran. Email: sedighehalavi54@gmail.com Journal Article 2021 07 22 It is proved that every locally flat Finsler manifold is a locally flat Riemannian manifold. Some low dimensional locally Finsler manifolds are classified. It is also proved that in a categorical sense, there is a correspondence between locally flat Finsler manifolds and locally hessian Riemannian manifolds Locally flat manifolds Finsler metric Bieberbach groups fourth root metric https://jfga.uma.ac.ir/article_1245_28136f81fc7aadef8127f9c8468d6837.pdf