On symmetric Willmore surfaces in spheres I: The orientation preserving case
On symmetric Willmore surfaces in spheres I: The orientation preserving case
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在球体中的对称威尔莫尔曲面上 I：方向保持情况
DOI：
10.1016/j.difgeo.2015.09.008
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发表时间：
2015
影响因子：
0.5
通讯作者：
Wang Peng
中科院分区：
文献类型：
--
作者：
Dorfmeister Josef;Wang Peng
本文系统地讨论了如何利用环群方法将方向保持对称性引入Willmore曲面的处理中，首先给出了Willmore曲面保持方向对称性的一般处理方法，然后给出了如何引入有限阶旋转对称性.对于球面上Willmore曲面的共形高斯映射的目标空间--对称空间，证明了球面上所有紧致Willmore曲面的共形高斯映射的亚纯不变势的存在性的长期猜想.我们还通过一些具体的例子来说明我们的结果。
In this paper we provide a systematic discussion of how to incorporate orientation preserving symmetries into the treatment of Willmore surfaces via the loop group method.In this context we first develop a general treatment of Willmore surfaces admitting orientation preserving symmetries, and then show how to induce finite order rotational symmetries. We also prove, for the symmetric space which is the target space of the conformal Gauss map of Willmore surfaces in spheres, the longstanding conjecture of the existence of meromorphic invariant potentials for the conformal Gauss maps of all compact Willmore surfaces in spheres. We also illustrate our results by some concrete examples.