Discrete curvature and the Gauss-Bonnet theorem
Mathematical Physics
2010-01-20 v1 High Energy Physics - Theory
math.MP
Quantum Algebra
Abstract
For matrix analogues of embedded surfaces we define discrete curvatures and Euler characteristics, and a non-commutative Gauss--Bonnet theorem is shown to follow. We derive simple expressions for the discrete Gauss curvature in terms of matrices representing the embedding coordinates, and provide a large class of explicit examples illustrating the new notions.
Keywords
Cite
@article{arxiv.1001.2223,
title = {Discrete curvature and the Gauss-Bonnet theorem},
author = {Joakim Arnlind and Jens Hoppe and Gerhard Huisken},
journal= {arXiv preprint arXiv:1001.2223},
year = {2010}
}