  We study rotational hypersurfaces with constant Gauss-Kronecker curvature. We
solve the ODE for the generating curves of such hypersurfaces and analyze
several geometric properties of such hypersurfaces. In particular, we discover
a class of non-compact rotational hypersurfaces with constant and negative
Gauss-Kronecker curvature and finite volume, which can be seen as the
higher-dimensional generalization of the pseudo-sphere. Finally we investigate
other types of rotational hypersurfaces with similar curvature constraints,
including those with prescribed Gauss-Kronecker curvature.
