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On the classical geometry of embedded manifolds in terms of Nambu brackets (1003.5981v1)
Published 31 Mar 2010 in math.DG, hep-th, math-ph, and math.MP
Abstract: We prove that many aspects of the differential geometry of embedded Riemannian manifolds can be formulated in terms of a multi-linear algebraic structure on the space of smooth functions. In particular, we find algebraic expressions for Weingarten's formula, the Ricci curvature and the Codazzi-Mainardi equations.
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