A note on the generalized Weierstrass representation
Differential Geometry
2007-05-23 v1 Mathematical Physics
math.MP
Abstract
The study of the relation between the Weierstrass inducing formulae for constant mean curvature surfaces and the completely integrable euclidean nonlinear sigma-model suggests a connection among integrable sigma -models in a background and other type of surfaces. We show how a generalization of the Weierstrass representation can be achieved and we establish a connection with the Weingarten surfaces. We suggest also a possible generalization for two-dimensional surfaces immersed in a flat space R^8 with Euclidean metric.
Keywords
Cite
@article{arxiv.math/0207261,
title = {A note on the generalized Weierstrass representation},
author = {L. Martina and Kur. Myrzakul and R. Myrzakulov},
journal= {arXiv preprint arXiv:math/0207261},
year = {2007}
}
Comments
8 pages, LateX