Induced surfaces and their integrable dynamics. II. Generalized Weierstrass representations in 4D spaces and deformations via DS hierarchy

1998/10/22 by B. G. Konopelchenko, Konopelchenko, B. G., G. Landolfi +1
Mathematics · Physics and Astronomy · #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #math.DG #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.math/9810138

LaTeX, 50 pages

arxiv created 1998/10/22 · arxiv updated 2009/11/30

Abstract

Extensions of the generalized Weierstrass representation to generic surfaces in 4D Euclidean and pseudo-Euclidean spaces are given. Geometric characteristics of surfaces are calculated. It is shown that integrable deformations of such induced surfaces are generated by the Davey -Stewartson hierarchy. Geometrically these deformations are characterized by the invariance of an infinite set of functionals over surface. The Willmore functional (the total squared mean curvature) is the simplest of them. Various particular classes of surfaces and their integrable deformations are considered.

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