Eikonal hypersurfaces in the Euclidean \(n\)-space
type: Item
instance of: scholarly article
title: Eikonal hypersurfaces in the Euclidean \(n\)-space
zbMATH Open document ID: 1387.53015
author: A. Yampolsky
published in: Mediterranean Journal of Mathematics
publication date: 2017-11-08T00:00:00Z
review text: 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''.
reviewed by: Raina Ivanova
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53B20
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 6803981
zbMATH Keywords: constant slope hypersurface
zbMATH Keywords: eikonal equation
MaRDI profile type: Publication
full work available at URL: s00009-017-0965-z
OpenAlex ID: W2728731459
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DOI: 10.1007/S00009-017-0965-Z
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description: scientific article; zbMATH DE number 6803981