The theorem of Fáry and Milnor for Hadamard manifolds
type: Item
instance of: scholarly article
title: The theorem of Fáry and Milnor for Hadamard manifolds
zbMATH Open document ID: 0922.57005
DOI: 10.1023/A:1005090710096
author: Carsten Schmitz
published in: Geometriae Dedicata
publication date: 1999-10-08T00:00:00Z
review text: The author shows that the total curvature of a knotted curve lying in a 3-dimensional Hadamard manifold is greater or equal to \(4\phi \). In the proof, he adapts to Hadamard manifolds the work by \textit{E. Pannwitz} [Math. Ann. 108, 629-672 (1933; Zbl 0007.23104)] for a knotted curve in Euclidean space \(E^n\).
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 53A35
zbMATH DE Number: 1180667
zbMATH Keywords: Hadamard manifold
zbMATH Keywords: total curvature
zbMATH Keywords: knotted curve
reviewed by: Maria do Rosário Pinto
MaRDI profile type: Publication
full work available at URL: a:1005090710096
OpenAlex ID: W167607893
description: scientific article; zbMATH DE number 1180667