Classification of surfaces with pointwise planar normal sections and its application to Fomenko's conjecture
type: Item
instance of: scholarly article
title: Classification of surfaces with pointwise planar normal sections and its application to Fomenko's conjecture
zbMATH Open document ID: 0587.53006
DOI: 10.1007/BF01221004
published in: Journal of Geometry
publication date: 1986-01-01T00:00:00Z
review text: Let \(\gamma\) be the intersection curve of a surface M in \(E^ m\) with a hyperplane H continuing the normal space of M at \(p\in M\). If the first 3 derivatives of \(\gamma\) are linearly dependent for each choice of p and H, then M has pointwise planar normal sections. The authors show that then M is either locally in \(E^ 3\) or an open portion of a Veronese surface in \(E^ 5\) or a standard torus \(S^ 1\times S^ 1\) in \(E^ 4\).
Mathematics Subject Classification ID: 53A07
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 3942368
zbMATH Keywords: planar normal sections
zbMATH Keywords: Veronese surface
Wikidata QID: Q123117954
author: Bang-Yen Chen
author: Shijie Li
reviewed by: Dirk Ferus
MaRDI profile type: Publication
cites work: Q3945159
cites work: Differential geometry of submanifolds with planar normal sections
cites work: Classification of surfaces with planar normal sections
cites work: SOME PROPERTIES OF TWO-DIMENSIONAL SURFACES WITH ZERO NORMAL TORSION IN $E^4$
cites work: Characterization and examples of Chen submanifolds
cites work: Q3679831
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description: scientific article; zbMATH DE number 3942368