On the classical geometry of embedded manifolds in terms of Nambu brackets
Differential Geometry
2010-04-01 v1 High Energy Physics - Theory
Mathematical Physics
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.
Keywords
Cite
@article{arxiv.1003.5981,
title = {On the classical geometry of embedded manifolds in terms of Nambu brackets},
author = {Joakim Arnlind and Jens Hoppe and Gerhard Huisken},
journal= {arXiv preprint arXiv:1003.5981},
year = {2010}
}
Comments
14 pages