论文标题
共形差异和谐波图中的共形表面几何形状
Quartic differentials and harmonic maps in conformal surface geometry
论文作者
论文摘要
我们考虑了伪形式几何形状中的编码2球体一致性，这些几何形状相对于正交表面的共形结构是谐波的。我们表征了诸如$ s $ willmore表面，准界面表面，3维空间形式的恒定平均曲率表面或3维均值曲率的恒定曲率表面的正交表面。然后，在这种情况下，我们研究了科比的四分位差异，并在考虑到所考虑的表面是超符号或正交的，与编辑2球的谐波一致性时，通常这通常是无分歧的。然后，我们可以将先前的结果应用于具有此类属性的表面。
We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. We characterise the orthogonal surfaces of such congruences as either $S$-Willmore surfaces, quasi-umbilical surfaces, constant mean curvature surfaces in 3-dimensional space forms or surfaces of constant lightlike mean curvature in 3-dimensional lightcones. We then investigate Bryant's quartic differential in this context and show that generically this is divergence free if and only if the surface under consideration is either superconformal or orthogonal to a harmonic congruence of codimension 2 spheres. We may then apply the previous result to characterise surfaces with such a property.
