Translationsflächen in der äquiaffinen Differentialgeometrie. (Translation surfaces in equiaffine differential geometry)
type: Item
instance of: scholarly article
title: Translationsflächen in der äquiaffinen Differentialgeometrie. (Translation surfaces in equiaffine differential geometry)
zbMATH Open document ID: 0732.53007
DOI: 10.1007/BF01225881
author: H. Pabel
published in: Journal of Geometry
publication date: 1991-01-01T00:00:00Z
review text: In this interesting paper the author investigates affine surfaces of translation and classifies special subclasses (affine minimal surfaces; surfaces of vanishing affine Gauss-Kronecker curvature; surfaces with only one family of affine lines of curvature). For the affine minimal surfaces of translation there existed so far 3 partial classifications [\textit{E. Glässner}, Arch. Math. 28, 436-439 (1977; Zbl 0359.53004); \textit{F. Manhart}, ibid. 44, 547-556 (1985; Zbl 0587.53009); \textit{L. Verstraelen} and \textit{L. Vrancken}, Mich. Math. J. 36, 77-93 (1989; Zbl 0677.53007)] and one complete, but unpublished classification by G. Penn (1989).
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53A10
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 4210956
zbMATH Keywords: affine spheres
zbMATH Keywords: affine surfaces of translation
zbMATH Keywords: affine minimal surfaces
reviewed by: Udo Simon
MaRDI profile type: Publication
cites work: Convex affine maximal surfaces
cites work: Ein Affinanalogon zu den Scherkschen Minimalflächen
cites work: Relative and affine normals
cites work: Die Affinminimalrückungsflächen
cites work: On the geometry of affine immersions
cites work: Q5790262
full work available at URL: https://doi.org/10.1007/bf01225881
OpenAlex ID: W2913603155
description: scientific article; zbMATH DE number 4210956