On the classical geometry of embedded surfaces in terms of Poisson brackets
Differential Geometry
2010-01-13 v1 Mathematical Physics
math.MP
Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.1001.1604,
title = {On the classical geometry of embedded surfaces in terms of Poisson brackets},
author = {Joakim Arnlind and Jens Hoppe and Gerhard Huisken},
journal= {arXiv preprint arXiv:1001.1604},
year = {2010}
}