TY - JOUR
T1 - Total curvature of graphs in Euclidean spaces
AU - Taniyama, Kouki
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
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
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U2 - 10.1016/S0926-2245(98)00002-3
DO - 10.1016/S0926-2245(98)00002-3
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 -