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arXiv · 1003.5981

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

Joakim Arnlind·Jens Hoppe·Gerhard Huisken
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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.

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Joakim Arnlind, Jens Hoppe, Gerhard Huisken. 2010-03-31. On the classical geometry of embedded manifolds in terms of Nambu brackets. https://arxiv.org/abs/1003.5981

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