On the classical geometry of embedded manifolds in terms of Nambu brackets

Details On the classical geometry of embedded manifolds in terms of Nambu brackets On the classical geometry of embedded manifolds in terms of Nambu brackets

2010-03-31

arxiv.org/abs/1003.5981v1

Mathematics

Differential Geometry

14 pages

Scientific paper

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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