Dynamics of Induced Surfaces in Four-Dimensional Euclidean Space

Details Dynamics of Induced Surfaces in Four-Dimensional Euclidean Space Dynamics of Induced Surfaces in Four-Dimensional Euclidean Space

2006-12-15

arxiv.org/abs/math-ph/0612050v1

Pacific J.Math.1:207-220,2008

Physics

Mathematical Physics

19 pages

Scientific paper

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.

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