Eikonal hypersurfaces in the Euclidean \(n\)-space
In this elegantly written paper the author proposes a new characterization of constant slope hypersurfaces \(F^n \subset E^{n+1}\). He proves that ``a hypersurface in \(E^n\) is of constant slope if and only if its normalized position vector provides a solution of the eikonal equation of the unit sphere''. The previously known Munteanu construction is generalized and an ``explicit parametric equation of the constant slope hypersurface is given''. It is also shown that ``the constant slope hypersurfaces are based on the polar pair of hypersurfaces in the unit sphere''.
scientific article; zbMATH DE number 6803981
scientific article