Hypersurfaces associated to Sn by a sphere congruence

Authors

DOI:

https://doi.org/10.17268/sel.mat.2019.02.09

Keywords:

Sphere congruence, envelope of a sphere congruence, surfaces associated by a sphere congruence

Abstract

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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Published

2019-12-24

How to Cite

Pereira Santos, L. R. (2019). Hypersurfaces associated to Sn by a sphere congruence. Selecciones Matemáticas, 6(02), 225-237. https://doi.org/10.17268/sel.mat.2019.02.09