Open Access
Translator Disclaimer
2002 Curvature Testing in 3-Dimensional Metric Polyhedral Complexes
Murray Elder, Jon McCammond
Experiment. Math. 11(1): 143-160 (2002).


In a previous article, the authors described an algorithm to determine whether a finite metric polyhedral complex satisfied various local curvature conditions such as being locally CAT(0). The proof made use of Tarski's theorem about the decidability of first order sentences over the reals in an essential way, and thus it was not immediately applicable to a specific finite complex. In this article, we describe an algorithm restricted to 3-dimensional complexes which uses only elementary 3-dimensional geometry. After describing the procedure, we include several examples involving Euclidean tetrahedra which were run using an implementation of the algorithm in GAP.


Download Citation

Murray Elder. Jon McCammond. "Curvature Testing in 3-Dimensional Metric Polyhedral Complexes." Experiment. Math. 11 (1) 143 - 160, 2002.


Published: 2002
First available in Project Euclid: 10 July 2003

zbMATH: 1042.20030
MathSciNet: MR1960308

Primary: 20F65
Secondary: 20F67

Keywords: CAT(0) , Non-positive curvature

Rights: Copyright © 2002 A K Peters, Ltd.


Vol.11 • No. 1 • 2002
Back to Top