Discrete curvature and the Gauss-Bonnet theorem

2010/01/13 by Joakim Arnlind, Arnlind, Joakim, Jens Hoppe +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.48550/arxiv.1001.2223

arxiv created 2010/01/13 · openalex publication_date 2010/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Cited by

• Curvature and gravity actions for matrix models: II. The case of general Poisson structures

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