Total curvature of graphs in Euclidean spaces

Kouki Taniyama*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1998 Apr
Externally publishedYes


  • Total curvature of graphs

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Computational Theory and Mathematics


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