Generalized Weierstrass representation for surfaces in multi-dimensional Riemann spaces

DOI10.1016/S0393-0440(98)00046-1zbMath0954.53011arXivmath/9804144OpenAlexW2048699554MaRDI QIDQ1299201

B. G. Konopelchenko, Giulio Landolfi

Publication date: 8 February 2001

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9804144

zbMATH Keywords

Weierstrass representationconformal immersionimmersed surface

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Local submanifolds (53B25)

Related Items (17)

Solutions of the Generalized Weierstrass Representation in Four-Dimensional Euclidean Space ⋮ Weierstrass representation for timelike surfaces in Minkowski 4-space ⋮ A cohomological approach to immersed submanifolds via integrable systems ⋮ On CP 1 and CP 2 Maps and Weierstrass Representations for Surfaces Immersed into Multi-Dimensional Euclidean Spaces ⋮ The generalized Weierstrass system and an application to the study of deformations of surfaces by means of integrable hierarchies ⋮ Weierstrass representation for discrete isotropic surfaces in \(\mathbb R^{2,1}\), \(\mathbb R^{3,1}\), and \(\mathbb R^{2,2}\) ⋮ Spinorial representation of submanifolds in Riemannian space forms ⋮ On the spinorial representation of spacelike surfaces into 4-dimensional Minkowski space ⋮ A condition for a closed one-form to be exact ⋮ Weierstrass Representation of Lightlike Surfaces in Lorentz-Minkowski 4-Space ⋮ Generalized Weierstrass representation for surfaces in terms of Dirac-Hestenes spinor field ⋮ Generalized Weierstrass relations and Frobenius reciprocity ⋮ A note on modified Veselov-Novikov hierarchy ⋮ Gross-Neveu models, nonlinear Dirac equations, surfaces and strings ⋮ Torus solutions to the Weierstrass-Enneper representation of surfaces ⋮ Weierstrass representation for lightlike surfaces in Lorentz-Minkowski 3-space ⋮ On Vortex Solutions and Links between the Weierstrass System and the Complex Sine-Gordon Equations

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• GENERALIZED WEIERSTRASS-ENNEPER INDUCING, CONFORMAL IMMERSIONS, AND GRAVITY
• KLEINIAN GEOMETRY AND THE N = 2 SUPERSTRING
• The Gauss Map of Surfaces in R³ and R⁴
• Constant mean curvature surfaces via an integrable dynamical system
• The global Weierstrass representation and its spectrum
• Modified Novikov--Veselov equation and differential geometry of surfaces
• Induced Surfaces and Their Integrable Dynamics

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