Centroaffine space curves with constant curvatures and homogeneous surfaces
type: Item
instance of: scholarly article
title: Centroaffine space curves with constant curvatures and homogeneous surfaces
zbMATH Open document ID: 1252.53008
author: Na Hu
published in: Journal of Geometry
publication date: 2012-07-10T00:00:00Z
review text: The present paper contributes to the differential geometry of the three dimensional centroaffine space, that is, the study of objects invariant by affine transformations in \({\mathbb R}^3\) fixing the origin. The authors give a classification of curves with constant centroaffine curvatures which leads to four types of solutions. As in the Euclidean situation, these curves are centroaffine and homogeneous, that means, they are orbits of one parameter subgroups of \(\mathrm{GL}(3,\mathbb R)\). Furthermore, in three cases, the authors find a centroaffine homogeneous surface carrying the curve.
reviewed by: Friedrich Manhart
Mathematics Subject Classification ID: 53A15
zbMATH DE Number: 6054111
zbMATH Keywords: centroaffine space curves
zbMATH Keywords: centroaffine homogeneous curves
zbMATH Keywords: centroaffine homogeneous surfaces
zbMATH Keywords: centroaffine curvatures
MaRDI profile type: Publication
full work available at URL: s00022-012-0105-7
OpenAlex ID: W1968947617
cites work: When Does the Position Vector of a Space Curve Always Lie in Its Rectifying Plane?
cites work: The fundamental theorems of curves and hypersurfaces in centro-affine geometry
cites work: Centroaffinely homogeneous surfaces in \(\mathbb{R}^ 3\)
cites work: Q4846450
cites work: Q5288993
cites work: Centroaffine minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
DOI: 10.1007/S00022-012-0105-7
description: scientific article; zbMATH DE number 6054111