Affine embeddings of flat compact manifolds. I
type: Item
instance of: scholarly article
title: Affine embeddings of flat compact manifolds. I
zbMATH Open document ID: 0666.53030
DOI: 10.1007/BF00128021
published in: Annals of Global Analysis and Geometry
publication date: 1987-01-01T00:00:00Z
review text: The aim of this paper is to construct affine embeddings of compact flat manifolds M with cyclic holonomy group of prime order p, called \(Z_ p\)- manifolds, into Euclidean space. First of all, the author shows that every compact flat manifold has the structure of a real affine variety and gives an explicit set of generators of the affine algebra of a \(Z_ p\)-manifold. Then he constructs affine embeddings of all \(Z_ 2\)- manifolds by means of generators of the affine algebra.
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 4090300
zbMATH Keywords: cyclic holonomy group
zbMATH Keywords: real affine variety
zbMATH Keywords: \(Z_ p\)-manifold
zbMATH Keywords: affine embeddings
author: Franz Pedit
MaRDI profile type: Publication
cites work: Über die Einbettung hyperbolischer Räume in euklidische Räume
cites work: Q5607044
cites work: The Gauss equations and rigidity of isometric embeddings
cites work: Compact flat Riemannian manifolds. I
cites work: On the Foundations of Combinatorial Theory. VII: Symmetric Functions through the Theory of Distribution and Occupancy
cites work: Isometrische Immersionen des \(n\)-dim. hyperbolischen Raumes \(H^n\) in \(E^{4n-3}\)
cites work: The imbedding problem for Riemannian manifolds
cites work: Q3858456
cites work: Hopf tori in \(S^ 3\)
cites work: On the Gauss equation of an isometric immersion
cites work: Q5546515
full work available at URL: https://doi.org/10.1007/bf00128021
OpenAlex ID: W1973073076
description: scientific article; zbMATH DE number 4090300