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  On the classical geometry of embedded surfaces in terms of Poisson brackets

Arnlind, J., Hoppe, J., & Huisken, G. (in preparation). On the classical geometry of embedded surfaces in terms of Poisson brackets.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-BD34-6 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0012-BD36-2
Genre: Paper

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1001.1604 (Preprint), 145KB
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File downloaded from arXiv at 2010-06-16 10:02
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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, escidoc:persistent22              
2Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24012              

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Free keywords: Mathematics, Differential Geometry, math.DG,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,Mathematics, Symplectic Geometry, math.SG
 Abstract: We consider surfaces embedded in a Riemannian manifold of arbitrary dimension and prove that many aspects of their differential geometry can be expressed in terms of a Poisson algebraic structure on the space of smooth functions of the surface. In particular, we find algebraic formulas for Weingarten's equations, the complex structure and the Gaussian curvature.

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 Dates: 2010-01-11
 Publication Status: Not specified
 Pages: -
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 Rev. Method: -
 Identifiers: arXiv: 1001.1604
URI: http://arxiv.org/abs/1001.1604
 Degree: -

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