Ruled surfaces with vanishing second Gaussian curvature
type: Item
instance of: scholarly article
title: Ruled surfaces with vanishing second Gaussian curvature
zbMATH Open document ID: 0765.53003
DOI: 10.1007/BF01641765
author: David E. Blair
author: T. Koufogiorgos
published in: Monatshefte für Mathematik
publication date: 1993-05-12T00:00:00Z
full work available at URL: https://eudml.org/doc/178558
review text: For a surface free of points of vanishing Gaussian curvature in Euclidean space the second Gaussian curvature is defined formally. It is first pointed out that a minimal surface has vanishing second Gaussian curvature but that a surface with vanishing second Gaussian curvature need not be minimal. Ruled surfaces for which a linear combination of the second Gaussian curvature and the mean curvature is constant along the rulings are then studied. In particular the only ruled surface in Euclidean space with vanishing second Gaussian curvature is a piece of a helicoid.
reviewed by: David E. Blair
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 164941
zbMATH Keywords: ruled surfaces
zbMATH Keywords: second Gaussian curvature
zbMATH Keywords: minimal surface
zbMATH Keywords: mean curvature
MaRDI profile type: Publication
cites work: Q4039783
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description: scientific article; zbMATH DE number 164941