Total curvature of graphs in Euclidean spaces
type: Item
instance of: scholarly article
title: Total curvature of graphs in Euclidean spaces
zbMATH Open document ID: 0924.53004
DOI: 10.1016/S0926-2245(98)00002-3
author: Kouki Taniyama
published in: Differential Geometry and its Applications
publication date: 1998-08-10T00:00:00Z
review text: We define the total curvature of a polygonal map from a finite graph \(G\) to a Euclidean space \(E^n\). We characterize for certain \(G\) the polygonal maps with minimal total curvature. When \(G\) is homeomorphic to a circle, the result is the piecewise linear version of the generalized Fenchel theorem on the total curvature of a smooth closed curve in a Euclidean space.
Mathematics Subject Classification ID: 53A04
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 53C42
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1186366
zbMATH Keywords: total curvature of graphs
zbMATH Keywords: Euclidean space
zbMATH Keywords: generalized Fenchel theorem
zbMATH Keywords: total curvature of a smooth closed curve
MaRDI profile type: Publication
Wikidata QID: Q115337524
cites work: Q5795778
cites work: Sur la courbure totale d'une courbe gauche faisant un nœud
cites work: Q3211984
cites work: Homeomorphic Continuous Curves in 2-Space are Isotopic in 3-Space
cites work: On the total curvature of knots
full work available at URL: s0926-2245(98)00002-3
OpenAlex ID: W2047801307
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description: scientific article; zbMATH DE number 1186366