An introduction to integrable difference and differential geometries: Affine spheres, their natural generalization and discretization
type: Item
instance of: scholarly article
zbMATH Open document ID: 1002.53005
publication date: 2003-01-20T00:00:00Z
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 1721617
zbMATH Keywords: affine sphere
zbMATH Keywords: Tzitzeica transformation
zbMATH Keywords: Bäcklund transformation
author: W. K. Schief
MaRDI profile type: Publication
title: An introduction to integrable difference and differential geometries: Affine spheres, their natural generalization and discretization
review text: The main goal of the paper is discretization of affine geometries. In 1907 Tzitzeica introduced the classical (proper) affine spheres. It is shown how these surfaces may be discretized in a natural geometric manner. The construction results in an integrable discrete version of the Tzitzeica-equation related to affine spheres. It is demonstrated how discrete surfaces may be generated by application of the Tzitzeica transformation to affine spheres. These discrete surfaces contain the class of discrete affine spheres constructed in the above mentioned geometric manner. As a by-product, a discrete version of the Tzitzeica transformation is obtained.NEWLINENEWLINEFor the entire collection see [Zbl 0974.00040].
reviewed by: Friedrich Manhart
description: scientific article; zbMATH DE number 1721617