常中曲率环面作为Davey-Stewartson方程的定常解
Constant mean curvature tori as stationary solutions to the Davey-Stewartson equation
摘要：
Da Rios和Levi-Civita的一个著名的结果是，一个封闭的平面曲线是弹性的，当且仅当它在局域感应（或烟圈）方程下是平稳的，其中平稳意味着在局域感应方程下的演化是通过刚性运动。我们证明了曲面的一个类似结果：环面浸入共形3-球面中关于空间型子几何具有常数中曲率当且仅当它在Davey-Stewartson流下是静止的。
英文摘要：
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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