Abstract
We prove 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 on the unit sphere. Explicit parametric equation of the constant slope hypersurface is given. We show that the constant slope hypersurfaces are based on the polar pair of hypersurfaces in the unit sphere.
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The author thanks the referee for the remarks and K. Drach (Jacobs University Bremen) for the useful discussions.
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Yampolsky, A. Eikonal Hypersurfaces in the Euclidean n-Space. Mediterr. J. Math. 14, 160 (2017). https://doi.org/10.1007/s00009-017-0965-z
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DOI: https://doi.org/10.1007/s00009-017-0965-z