Spacelike isoparametric hypersurfaces

Abstract

We generalise Ferus' work to study isoparametric hypersurfaces in semi-Riemannian space forms focusing, in this particular case, on anti-De Sitter spaces. We will show that two is an upper bound for the number of principal curvatures in a spacelike isoparametric hypersurface in the anti-De Sitter space. This fact will lead us to deduce a partial classification of isoparametric hypersurfaces in anti-De Sitter spaces.