Cayley surfaces in affine differential geometry
type: Item
instance of: scholarly article
title: Cayley surfaces in affine differential geometry
zbMATH Open document ID: 0684.53011
author: Katsumi Nomizu
author: Ulrich Pinkall
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1989-01-01T00:00:00Z
review text: A Cayley surface in affine space \({\mathbb{R}}^ 3\) is, by definition, the graph of a cubic polynomial, say, \(z=xy-y^ 3/3\quad or\quad z=xy-x^ 3/3.\) The purpose of the present paper is to characterize a Cayley surface as a nondegenerate surface in \({\mathbb{R}}^ 3\) whose cubic form in nonzero and parallel relative to the induced connection of the surface.
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 4120918
zbMATH Keywords: Cayley surface
zbMATH Keywords: cubic polynomial
zbMATH Keywords: cubic form
zbMATH Keywords: induced connection
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227729
OpenAlex ID: W2046363907
Wikidata QID: Q115227231
cites work: Q5725219
cites work: On completeness in affine differential geometry
cites work: On the geometry of affine immersions
cites work: Cubic form theorem for affine immersions
DOI: 10.2748/TMJ/1178227729
description: scientific article; zbMATH DE number 4120918