Eikonal Hypersurfaces in the Euclidean n-Space

Eikonal Hypersurfaces in the Euclidean n-Space We prove that a hypersurface in $$E^n$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

Eikonal Hypersurfaces in the Euclidean n-Space

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Publisher
Springer International Publishing
Copyright
Copyright © 2017 by Springer International Publishing AG
Subject
Mathematics; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-017-0965-z
Publisher site
See Article on Publisher Site

Abstract

We prove that a hypersurface in $$E^n$$ 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.

Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Jul 6, 2017

References

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