Surfaces via spinors and soliton equations

  • Iskander A. Taimanov

    Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia, and Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia
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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.