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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scharlau, Rudolf / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard

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IMPACT FACTOR 2017: 0.734

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1615-7168
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Volume 13, Issue 3

Issues

Hypersurfaces of revolution with proportional principal curvatures

Vincent Coll / Michael Harrison
Published Online: 2013-07-11 | DOI: https://doi.org/10.1515/advgeom-2012-0035

Abstract

We classify hypersurfaces of revolution for which the principal curvatures are proportional. These hypersurfaces form a one-parameter family indexed by the reals. The subsequent classification unites at least two important families of hypersurfaces of revolution: the generalized catenoids and the equizonal ovaloids.

Keywords: Catenoid; equizonal ovaloids; hypersurfaces; hypersurfaces of revolution; minimal hypersurfaces; principal curvature

About the article

Published Online: 2013-07-11

Published in Print: 2013-07-01


Citation Information: Advances in Geometry, Volume 13, Issue 3, Pages 485–496, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2012-0035.

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Citing Articles

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[1]
Jacob Blackwood, Adam Dukehart, and Mohammad Javaheri
Involve, a Journal of Mathematics, 2017, Volume 10, Number 3, Page 465
[2]
Vincent Coll and Mike Harrison
The American Mathematical Monthly, 2014, Volume 121, Number 2, Page 109

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