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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
Published Online: 2013-07-11
Published in Print: 2013-07
© 2013 by Walter de Gruyter GmbH & Co.