Constant mean curvature tori as stationary solutions to the Davey-Stewartson equation (Q431278)

This paper deals with a generalization of the relation between the nonlinear Schrödinger equation and the motion of vortex filaments in \({\mathbb R}^3\). It studies an ``analogous geometric version of the Davey-Stewartson flow as an evolution of surfaces in 4-space'' (cf., e.g., [\textit{B. G. Konopelchenko}, Ann. Global Anal. Geom. 18, No. 1, 61--74 (2000; Zbl 0946.53002)]). The main result gives a ``Möbius geometric characterization of constant mean curvature tori in space forms as stationary solutions of the Davey-Stewartson equation''. An appendix records a private communication of K. Voss that ``seems to be nowhere published'', and that gives a local ``characterization of Willmore surfaces and constant mean curvature surfaces in space forms''.