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Discrete curvature and the Gauss-Bonnet theorem

MPS-Authors
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Arnlind,  Joakim
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Hoppe,  Jens
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Huisken,  Gerhard
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1001.2223
(Preprint), 175KB

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Citation

Arnlind, J., Hoppe, J., & Huisken, G. (in preparation). Discrete curvature and the Gauss-Bonnet theorem.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-B7F3-C
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.