Discrete curvature and the Gauss-Bonnet theorem

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.

References in corpus (2)

• Representation theory of C-algebras for a higher order class of spheres and tori
• On the classical geometry of embedded surfaces in terms of Poisson brackets

Cited by in corpus (7)

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• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
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• On the geometry of Kähler-Poisson structures
• Quasi-Static BMN Solutions
• Matrix regularization of embedded 4-manifolds