论文标题
$ \ mathbb {c}^2 $中的真实椭圆形的cr脐带基因座
The CR umbilical locus of a real ellipsoid in $\mathbb{C}^2$
论文作者
论文摘要
本文涉及$ \ mathbb {c}^2 $中真实椭圆形的Cr脐带基因座，该点可以通过球体的生物形态图像（最多为6阶）进行移动的一组点。 Huang和Ji证明了这个基因座是非空的。 Ebenfelt和Zaitsev证明，对于足够“封闭”球体的椭圆形，该基因座实际上包含脐点的“稳定”曲线。 Foo，Merker和TA随后提供了其中包含的明确曲线。本文的主要结果表明，脐带基因座是上面提到的曲线的结合，也是一个非平凡的真实品种，该品种由两个实际变量的两个均匀的真实六个方程定义。当有相等的半轴对成对时，其中之一是使我们明确确定基因座的因素。
This paper concerns the CR umbilical locus of a real ellipsoid in $\mathbb{C}^2$, the set of points at which the ellipsoid can be osculated by a biholomorphic image of the sphere up to 6th order. Huang and Ji proved that this locus is non-empty. Ebenfelt and Zaitsev proved that, for ellipsoids that are sufficiently "closed" to the sphere, the locus actually contains a "stable" curve of umbilical points. Foo, Merker and Ta later provided an explicit curve that is contained in it. The main result in this paper exhibits that the umbilical locus is the union of the curves mentioned above and a non-trivial real variety which is defined by two homogeneous real sextic equations of four real variables. When there are suitable pairs of equal semi-axes, one of them factors allowing us to determine the locus explicitly.
