Discrete curvature and the Gauss-Bonnet theorem

Details Discrete curvature and the Gauss-Bonnet theorem Discrete curvature and the Gauss-Bonnet theorem

2010-01-13

arxiv.org/abs/1001.2223v1

Physics

Mathematical Physics

Scientific paper

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.

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