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  Discrete curvature and the Gauss-Bonnet theorem

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

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-B7F3-C Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-B7F7-4
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1001.2223 (Preprint), 175KB
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File downloaded from arXiv at 2010-05-27 13:47
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 Creators:
Arnlind, Joakim1, Author              
Hoppe, Jens2, Author
Huisken, Gerhard2, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, escidoc:persistent22              
2Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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Free keywords: Mathematical Physics, math-ph,High Energy Physics - Theory, hep-th,Mathematics, Mathematical Physics, math.MP,Mathematics, Quantum Algebra, math.QA
 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.

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 Dates: 2010-01-13
 Publication Status: Not specified
 Pages: -
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 Rev. Method: -
 Identifiers: arXiv: 1001.2223
URI: http://arxiv.org/abs/1001.2223
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