General affine differential geometry for low codimension immersions
type: Item
instance of: scholarly article
title: General affine differential geometry for low codimension immersions
zbMATH Open document ID: 0621.53009
DOI: 10.1007/BF01159813
author: Steven Wilkinson
published in: Mathematische Zeitschrift
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/183752
review text: Given an immersion of an N-dimensional manifold into \((N+K)\)-dimensional general affine space, three affine invariant tensors are constructed on the manifold that depend, respectively, on the second, third, and fourth order information of the immersion. For \(K=2\), \(N>2\) it is proven that the first two tensors are sufficient to discern between two different affine immersions. For \(N=2=K\) and \(K=1\) it is proven that all three of the tensors are sufficient to discern between two affine immersions.
Mathematics Subject Classification ID: 53A15
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 4007140
zbMATH Keywords: immersion
zbMATH Keywords: affine invariant tensors
zbMATH Keywords: affine immersions
zbMATH Keywords: low codimension
Wikidata QID: Q115393988
MaRDI profile type: Publication
cites work: Zur affinen Differentialgeometrie. I. Über \(p\)-dimensionale Minimalflächen und Sphären im \(n\)-dimensionalen Raum. II. Über zweidimensionale Flächen im vierdimensionalen Raum
cites work: Der Berührungstensor zweier Flächen und die Affingeometrie der \(F_p\) im \(A_n\). I
cites work: Der Berührungstensor zweier Flächen und die Affingeometrie der \(F_p\) im \(A_n\). II
OpenAlex ID: W1964754587
description: scientific article; zbMATH DE number 4007140