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

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

2010-01-11

arxiv.org/abs/1001.1604v1

Mathematics

Differential Geometry

Scientific paper

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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