Intrinsic equations for a relaxed elastic line on an oriented surface
type: Item
instance of: scholarly article
title: Intrinsic equations for a relaxed elastic line on an oriented surface
zbMATH Open document ID: 0647.53002
DOI: 10.1007/BF00151344
author: H. K. Nickerson
author: Gerald S. Manning
published in: Geometriae Dedicata
publication date: 1988-01-01T00:00:00Z
review text: A regular arc on an oriented surface in 3-space is called a relaxed elastic line on that surface if it realizes an extremum of the total square (spatial) curvature among all arcs on the surface with the same initial point and the same initial direction. Extending work of the second author [Q. Appl. Math. 45, 515-527 (1987; Zbl 0633.73023)], the intrinsic equations for relaxed elastic lines on surfaces are derived. In a plane or on a sphere the relaxed elastic lines are given exactly by the geodesics. This property is shown to characterize parts of planes or spheres. On other surfaces there exist relaxed elastic lines which are not geodesics.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 4056445
zbMATH Keywords: total square curvature
zbMATH Keywords: relaxed elastic line
zbMATH Keywords: surface
zbMATH Keywords: geodesics
reviewed by: Bernd Wegner
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00151344
OpenAlex ID: W2058862829
description: scientific article; zbMATH DE number 4056445