Weierstrass representations for surfaces in 4D spaces and their integrable deformations via DS hierarchy
arXiv:math/9807129
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.
Latex, 18 pages
References in corpus (5)
- Constant mean curvature surfaces via integrable dynamical system
- Generalized Weierstrass representation for surfaces in multidimensional Riemann spaces
- Conformal invariant functionals of immersions of tori into R^3
- On classical string configurations
- Dirac Operator of a Conformal Surface Immersed in R^4: Further Generalized Weierstrass Relation
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- Constant mean curvature tori as stationary solutions to the Davey-Stewartson equation
- Surfaces via spinors and soliton equations
- Spinor Representations of Surfaces in 4-Dimensional Pseudo-Riemannian Manifolds
- Dirac-Hestenes spinors and Weierstrass representation for surfaces in 4D complex space
- Spinor Fields on the Surface of Revolution and their Integrable Deformations via the mKdV-Hierarchy
- Characterization of hypersurfaces in four dimensional product spaces via two different Spin structures