Abstract
In this paper, we classify the hypersurfaces in Sn×R and Hn×R, n≠3, with g distinct constant principal curvatures, g∈{1,2,3}, where Sn and Hn denote the sphere and hyperbolic space of dimension n, respectively. We prove that such hypersurfaces are isoparametric in those spaces. Furthermore, we find a necessary and sufficient condition for an isoparametric hypersurface in Sn×R and Hn×R with flat normal bundle when regarded as submanifolds with codimension two of the underlying flat spaces Rn+2⊃Sn×R and Ln+2⊃Hn×R, having constant principal curvatures.
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