Isoparametric hypersurfaces in Minkowski spaces

In this paper, we introduce isoparametric functions and isoparametric hypersurfaces in Finsler manifolds and give the necessary and sufficient conditions for a transnormal function to be isoparametric. We then prove that hyperplanes, Minkowski hyperspheres and F⁎F⁎-Minkowski cylinders in a Minkowski space with BH-volume (resp. HT-volume) form are all isoparametric hypersurfaces with one and two distinct constant principal curvatures respectively. Moreover, we give a complete classification of isoparametric hypersurfaces in Randers–Minkowski spaces.