Clifford-Wolf homogeneous Finsler metrics on spheres

An isometry of a Finsler space is called Clifford-Wolf translation (CW-translation) if it moves all points the same distance. A Finsler space $(M, F)$iscalledClifford-Wolfhomogeneous(CW-homogeneous)ifforany$x, y\in M$thereisaCW-translation$\sigma$suchthat$\sigma (x)=y$\mathrm{.}Weprovethatif$F$isahomogeneousFinslermetriconthesphere$S^n$suchthat$(S^n, F)$ is CW-homogeneous, then $F$ must be a Randers metric. This gives a complete classification of CW-homogeneous Finsler metrics on spheres.