Soliton Spheres
Soliton Spheres
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孤子球
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
G. Peters
中科院分区：
文献类型：
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作者：
C. Bohle;G. Peters
孤子球是浸入共形4-球S = HP中的2-球，它允许通过扭量投影和CP中有理曲线的对偶化获得有理的共形参数f：CP → HP。孤子球可以被描述为四元数Plücker估计中相等的情况。Taimanov引入的一类特殊的孤子球是具有旋转对称Weierstrass势的浸入到R中的孤子球，它通过R-AKNS线性问题与mKdV方程的孤子相关。我们表明，Willmore球和布莱恩特球光滑的结束是孤子球的进一步的例子。证明了3-球中孤子球的Willmore能量的可能值为W = 4 π d，其中d ∈ N {0，2，3，5，7}.对于上面提到的三种特殊类型的孤子球，同样的量子化以前是单独已知的。
Soliton spheres are immersed 2–spheres in the conformal 4–sphere S = HP that allow rational, conformal parametrizations f : CP → HP obtained via twistor projection and dualization from rational curves in CP. Soliton spheres can be characterized as the case of equality in the quaternionic Plücker estimate. A special class of soliton spheres introduced by Taimanov are immersions into R with rotationally symmetric Weierstrass potentials that are related to solitons of the mKdV–equation via the ZS–AKNS linear problem. We show that Willmore spheres and Bryant spheres with smooth ends are further examples of soliton spheres. The possible values of the Willmore energy for soliton spheres in the 3–sphere are proven to be W = 4πd with d ∈ N{0, 2, 3, 5, 7}. The same quantization was previously known individually for each of the three special classes of soliton spheres mentioned above.
从 2 圆环到 4 球体的共形映射
DOI：
10.1515/crelle.2011.156
发表时间：
2012
期刊：
影响因子：
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作者：
Leschke;Pinkall
通讯作者：
Pinkall