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Arnlind, Hoppe and Huisken showed how to express the Gauss and mean curvatureof a surface embedded in a Riemannian manifold in terms of Poisson brackets ofthe embedding coordinates. We generalize these expressions to thepseudo-Riemannian setting and derive explicit formulas for the case of surfacesembedded in $\R^m$ with indefinite metric.

The geometry of embedded pseudo-Riemannian surfaces in terms of Poisson brackets