2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141895Here, an extension of the Obata-Tanno's theorem to Finsler geometry is established and the following rigidity result is obtained; Every complete connected Finsler manifold of positive constant flag curvature is isometrically homeomorphic to an $n$-sphere equipped with a certain Finsler metric, and vise versa.8 pagesDifferential Geometry53C60 (Primary); 58B20 (Secondary)text