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Free keywords:
Mathematics, Differential Geometry, math.DG,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,Mathematics, Symplectic Geometry, math.SG
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.