Manifolds without \(\tfrac {1}{k}\)-geodesics
type: Item
instance of: scholarly article
title: Manifolds without \(\tfrac {1}{k}\)-geodesics
zbMATH Open document ID: 1163.53027
author: Wing Kai Ho
published in: Israel Journal of Mathematics
publication date: 2009-02-17T00:00:00Z
review text: Let M be a smooth hypersurface in the Euclidean space and \(\gamma: S^1\rightarrow M\) a closed geodesic parametrized by arc length and with length \(l\). Then \(\gamma\) is called a \(1/k\)-geodesic if it is distance minimizing on every segment of length \(l/k\). In the paper it is shown that for every integer \(k\geq 2\) there exists a smooth surface (a surface of revolution) \(M_k\) which has no \(1/k\)-geodesic.
reviewed by: Zdeněk Dušek
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53A05
zbMATH DE Number: 5508722
zbMATH Keywords: Riemannian manifold
zbMATH Keywords: surface in Euclidean space
zbMATH Keywords: geodesic
zbMATH Keywords: \(1/k\)-geodesic
MaRDI profile type: Publication
full work available at URL: s11856-008-1063-5
OpenAlex ID: W1019636958
cites work: Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu
cites work: Convergence and the length spectrum
cites work: Riemannian geometry and geometric analysis
cites work: Q4091004
cites work: Q4067705
cites work: Q3881473
DOI: 10.1007/S11856-008-1063-5
description: scientific article; zbMATH DE number 5508722