  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.
