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arXiv · 1001.1604

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

Joakim Arnlind·Jens Hoppe·Gerhard Huisken
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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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Joakim Arnlind, Jens Hoppe, Gerhard Huisken. 2010-01-11. On the classical geometry of embedded surfaces in terms of Poisson brackets. https://arxiv.org/abs/1001.1604

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