Relative and affine normals
type: Item
instance of: scholarly article
title: Relative and affine normals
zbMATH Open document ID: 0643.53008
DOI: 10.1007/BF03323244
author: Erhard Heil
published in: Results in Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Motivated by a well-known representation of the affine normal vector of a hypersurface in equi-affine differential geometry, the author defines a `Laplace normal' in relative differential geometry. It is obtained (up to a normalization) by applying the Laplace operator with respect to the first fundamental form of relative differential geometry to the position vector. The author shows that the Laplace normal can be interpreted as a relative normal with respect to a suitable gauge surface. The positions of relative and Laplace normals are discussed, especially for the cases of the Euclidean, equi-affine and centro-affine normalizations.
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 4048545
zbMATH Keywords: affine normal
zbMATH Keywords: relative differential geometry
zbMATH Keywords: Laplace operator
zbMATH Keywords: Laplace normal
reviewed by: Rolf Schneider
MaRDI profile type: Publication
cites work: Q5514233
cites work: Q3321051
cites work: Ricci-Calculus
description: scientific article; zbMATH DE number 4048545