Isoparametric functions on Finsler space forms

In this paper, we prove that transnormal functions are isoparametric functions on Finsler space forms (N©, F) under certain conditions, which generalize Theorem B given by Q.M. Wang in Riemannian case. Next, we discuss the relationship between umbilic hypersurfaces and isoparametric hypersurfaces in (N©, F). Further more, we construct a locally isoparametric function by a distance function and give a global isoparametric function on a standard Finsler sphere.