Dynamics of Induced Surfaces in Four-Dimensional Euclidean Space
Mathematical Physics
2010-02-03 v1 Differential Geometry
math.MP
Abstract
The Davey Stewartson hierarchy will be developed based on a set of three matrix differential operators. These equations will act as evolution equations for different types of surface deformation in Euclidean four space. The Weierstrass representation for surfaces will be developed and its uniqueness up to gauge transformations will be reviewed. Applications of the hierarchy will be given with regard to generating deformations of surfaces, and it will be shown that the Willmore functional is preserved under this kind of deformation.
Cite
@article{arxiv.math-ph/0612050,
title = {Dynamics of Induced Surfaces in Four-Dimensional Euclidean Space},
author = {Paul Bracken},
journal= {arXiv preprint arXiv:math-ph/0612050},
year = {2010}
}
Comments
19 pages