The classification of hypersurfaces of a Euclidean space with parallel higher order fundamental form
type: Item
instance of: scholarly article
title: The classification of hypersurfaces of a Euclidean space with parallel higher order fundamental form
zbMATH Open document ID: 0671.53007
DOI: 10.1007/BF02570761
published in: Mathematische Zeitschrift
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174152
review text: We show that a hypersurface of a Euclidean space \({\mathbb{R}}^{n+1}\) with parallel higher order fundamental form \((\nabla^ kh=0)\) is either parallel \((\nabla h=0)\), and therefore an open part of a hypersphere, a hyperplane, or a product of a sphere and an affine subspace, or else it is a cylinder on a plane curve whose curvature is a polynomial function of the arc length.
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 4098197
zbMATH Keywords: hypersurface
zbMATH Keywords: parallel higher order fundamental form
author: Franki Dillen
reviewed by: Franki Dillen
MaRDI profile type: Publication
cites work: Q4725274
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description: scientific article; zbMATH DE number 4098197