Weierstrass representations for surfaces in 4D spaces and their integrable deformations via DS hierarchy

1998/07/23 by B. G. Konopelchenko, Konopelchenko, B. G. · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Differential Geometry (math.DG) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons #math.DG #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.math/9807129

Latex, 18 pages

arxiv created 1998/07/23 · openalex publication_date 1998/07/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalized Weierstrass representations for generic surfaces conformally immersed into four-dimensional Euclidean and pseudo-Euclidean spaces of different signatures are presented. Integrable deformations of surfaces in these spaces generated by the Davey-Stewartson hierarchy of integrable equations are proposed. Willmore functional of a surface is invariant under such deformations.

Citations

• Dirac Operator of a Conformal Surface Immersed in R⁴: Further Generalized Weierstrass Relation

Cited by

• The Ozawa solution to the Davey--Stewartson II equations and surface theory

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