Hypersurfaces associated to Sn by a sphere congruence
DOI:
https://doi.org/10.17268/sel.mat.2019.02.09Keywords:
Sphere congruence, envelope of a sphere congruence, surfaces associated by a sphere congruenceAbstract
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.References
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