Total curvature of graphs in Euclidean spaces

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

In this paper we define the total curvature of a polygonal map from a finite graph G to a Euclidean space En. 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.

Original languageEnglish
Pages (from-to)135-155
Number of pages21
JournalDifferential Geometry and its Application
Volume8
Issue number2
Publication statusPublished - 1998 Apr
Externally publishedYes

Fingerprint

Total curvature
Euclidean space
Graph in graph theory
Closed curve
Finite Graph
Homeomorphic
Piecewise Linear
Circle
Theorem

Keywords

  • Total curvature of graphs

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Analysis
  • Geometry and Topology

Cite this

Total curvature of graphs in Euclidean spaces. / Taniyama, Kouki.

In: Differential Geometry and its Application, Vol. 8, No. 2, 04.1998, p. 135-155.

Research output: Contribution to journalArticle

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