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

Details Constant mean curvature tori as stationary solutions to the Davey-Stewartson equation Constant mean curvature tori as stationary solutions to the Davey-Stewartson equation

2008-10-07

arxiv.org/abs/0810.1238v1

Mathematics

Differential Geometry

10 pages

Scientific paper

A well known result of Da Rios and Levi-Civita says that a closed planar curve is elastic if and only if it is stationary under the localized induction (or smoke ring) equation, where stationary means that the evolution under the localized induction equation is by rigid motions. We prove an analogous result for surfaces: an immersion of a torus into the conformal 3-sphere has constant mean curvature with respect to a space form subgeometry if and only if it is stationary under the Davey-Stewartson flow.

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