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On the classical geometry of embedded manifolds in terms of Nambu brackets

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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;

/persons/resource/persons20689

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

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1003.5981
(Preprint), 192KB

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Citation

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


Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-9DE1-C
Abstract
We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of a multi-linear algebraic structure on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations.