### Abstract

In this paper 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.

Original language | English |
---|---|

Pages (from-to) | 135-155 |

Number of pages | 21 |

Journal | Differential Geometry and its Application |

Volume | 8 |

Issue number | 2 |

Publication status | Published - 1998 Apr |

Externally published | Yes |

### Fingerprint

### Keywords

- Total curvature of graphs

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Analysis
- Geometry and Topology

### Cite this

*Differential Geometry and its Application*,

*8*(2), 135-155.

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

Research output: Contribution to journal › Article

*Differential Geometry and its Application*, vol. 8, no. 2, pp. 135-155.

}

TY - JOUR

T1 - Total curvature of graphs in Euclidean spaces

AU - Taniyama, Kouki

PY - 1998/4

Y1 - 1998/4

N2 - 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.

AB - 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.

KW - Total curvature of graphs

UR - http://www.scopus.com/inward/record.url?scp=0032036344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032036344&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032036344

VL - 8

SP - 135

EP - 155

JO - Differential Geometry and its Applications

JF - Differential Geometry and its Applications

SN - 0926-2245

IS - 2

ER -