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

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

2011-07-04

arxiv.org/abs/1107.0700v1

Mathematics

Differential Geometry

6 pages

Scientific paper

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

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