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Mathematics > Differential Geometry

arXiv:2207.07856 (math)
[Submitted on 16 Jul 2022]

Title:Surfaces via spinors and soliton equations

Authors:Iskander A. Taimanov
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Abstract:This article surveys the Weierstrass representation of surfaces in the three- and four-dimensional spaces, with an emphasis on its relation to the Willmore functional. We also describe an application of this representation to constructing a new type of solutions to the Davey-Stewartson II equation. They have regular initial data, gain one-point singularities at certain moments of time, and extend to smooth solutions for the remaining times.
Comments: 18 pages
Subjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP); Exactly Solvable and Integrable Systems (nlin.SI)
Cite as: arXiv:2207.07856 [math.DG]
  (or arXiv:2207.07856v1 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.2207.07856
Journal reference: Proc. Int. Cong. Math. 2022, Vol.4, 2638-2654, EMS Press, Berlin, 2023
Related DOI: https://doi.org/10.4171/ICM2022/92

Submission history

From: Iskander A. Taimanov [view email]
[v1] Sat, 16 Jul 2022 07:05:43 UTC (14 KB)
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