On affine-maximal ruled surfaces
type: Item
instance of: scholarly article
title: On affine-maximal ruled surfaces
zbMATH Open document ID: 0754.53016
DOI: 10.1007/BF02571551
author: S. Singh
published in: Mathematische Zeitschrift
publication date: 1992-09-26T00:00:00Z
review text: In this paper the authors give a 2-parameter family \({\mathcal F}=\{M(\beta,\gamma)\mid \beta,\gamma: \mathbb{R}\to\mathbb{R}\) are functions\} of nondegenerate ruled surfaces, which are affine complete and have flat affine metric. Furthermore, they study the index of \(M(\beta,\gamma)\) and prove that a nondegenerate affine maximal surface with indefinite flat affine metric is locally affinely equivalent to \(M(\beta,\gamma)\).
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 54906
zbMATH Keywords: second variation
zbMATH Keywords: affine complete
zbMATH Keywords: flat affine metric
reviewed by: An-Min Li
MaRDI profile type: Publication
cites work: Hypersurfaces with Maximal Affinely Invariant Area
cites work: Q5820676
cites work: Q5848416
cites work: Flat affine spheres in \(R^ 3\)
cites work: On completeness in affine differential geometry
cites work: Cayley surfaces in affine differential geometry
cites work: Local classification of twodimensional affine spheres with constant curvature metric
cites work: Affine variation formulas and affine minimal surfaces
full work available at URL: https://doi.org/10.1007/bf02571551
OpenAlex ID: W1982627614
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description: scientific article; zbMATH DE number 54906