An analogue of the Sauer theorem.
type: Item
instance of: scholarly article
title: An analogue of the Sauer theorem.
zbMATH Open document ID: 1066.53008
DOI: 10.1023/A:1026123206174
author: V. T. Fomenko
published in: Mathematical Notes
publication date: 2004-12-02T00:00:00Z
review text: The theorem of \textit{R. Sauer} [Math. Ann. 111, 71--82 (1935; Zbl 0010.37402, JFM 61.0744.04)] asserts that between bending fields of two projectively equivalent surfaces in Euclidean space \(E^3\) a bijection can be established so that to the trivial shift fields of one surface correspond the trivial shift fields of the other surface. Here, an analogue is proven for simply connected surfaces \(F^2:{\mathbf r}={\mathbf r}(u, v)\), \((u,v)\in D\) of class \(C^2(D)\) in \(E^3\), where bending fields are replaced by infinitely small equi-areal deformations and bijection preserves the pointwise spherical map (i.e. for which the variation \(\delta{\mathbf n}\) of a normal unit vector field \({\mathbf n}\) is collinear to \({\mathbf n}\)).
Mathematics Subject Classification ID: 53A05
Mathematics Subject Classification ID: 30G20
zbMATH DE Number: 2121055
zbMATH Keywords: Sauer theorem
zbMATH Keywords: projectively equivalent surfaces
zbMATH Keywords: infinitely small equiareal deformations
zbMATH Keywords: G-deformations
reviewed by: Ülo Lumiste
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2121055