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

1998/01/04 by Shigeki Matsutani, Matsutani, Shigeki · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9801006

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arxiv created 1998/01/04 · openalex publication_date 1998/01/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac operator defined over a conformal surface immersed in R³ is identified with the Dirac operator which is generalized the Weierstrass- Enneper equation and Lax operator of the modified Novikov-Veselov (MNV) equation. In this article, I determine the Dirac operator defined over a conformal surface immersed in R⁴, which is reduced to the Lax operators of the nonlinear Schrodinger and the MNV equations by taking appropriate limits. Thus the Dirac operator might be the Lax operator of (2+1)- dimensional soliton equation.

Citations

• Closed curves in R³: a characterization in terms of curvature and torsion, the Hasimoto map and periodic solutions of the Filament Equation

Cited by

• Spinor Fields on the Surface of Revolution and their Integrable Deformations via the mKdV-Hierarchy
• Weierstrass representations for surfaces in 4D spaces and their integrable deformations via DS hierarchy

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