Isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in Finsler spaces

We study the relationship between isoparametric hypersurfaces and hypersurfaces with constant principal curvatures in non-Riemannian Finsler spaces. We give some examples of isoparametric hypersurfaces with (non)constant principal curvatures on Randers manifolds with nonconstant flag curvatures. Furthermore, we construct an example of a conformally flat Randers manifold which admits a family of nonisoparametric hyperplanes with constant principal curvatures.