Abstract
In this paper we consider $O(m)\times O(n)$-invariant parabolic hypersurfaces of Euclidean space with constant mean curvature. We analyse the orbit space of the $O(m)\times O(n)$-group on $\mathbb{R}^{m+n}$ to give some classification results of these hypersurfaces for which the Gauss-Kronecker curvature does not change its sign.
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