In this work a sufficient condition is exhibited for a hypersurface in Rn+1 to be the envelope of a sphere congruence whose other envelope is contained in a unit sphere. A local parametrization for such envelopes is provided depending on an orthogonal local parametrization of Sn and their fundamental forms are described. Finally, a necessary and sufficient condition is presented so that such hypersurfaces are parametrized by lines of curvature and so that they are of rotation.

In this work a sufficient condition is exhibited for a hypersurface in Rn+1 to be the envelope of a sphere congruence whose other envelope is contained in a unit sphere. A local parametrization for such envelopes is provided depending on an orthogonal local parametrization of Sn and their fundamental forms are described. Finally, a necessary and sufficient condition is presented so that such hypersurfaces are parametrized by lines of curvature and so that they are of rotation.