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- Title
Constant mean curvature tori as stationary solutions to the Davey-Stewartson equation.
- Authors
Bohle, Christoph
- Abstract
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.
- Subjects
EQUATIONS; CURVATURE; CALCULUS; MATHEMATICS; SPACES of measures
- Publication
Mathematische Zeitschrift, 2012, Vol 271, Issue 1/2, p489
- ISSN
0025-5874
- Publication type
Article
- DOI
10.1007/s00209-011-0873-z