论文标题
在高度退化的球形图上
On highly degenerate CR maps of spheres
论文作者
论文摘要
对于$ n \ geq 4 $，我们将三维单元球的$（n-3）$ - 脱位平滑的Cr地图分类为$（2N-1）$ - 尺寸单位球体。这些地图中的每一个都包含在五维复合线性空间中，最多占两个图像，或者等同于四维图中的四个图中的一个图像。作为我们分类的副产品，我们获得了第三级理性地图的新示例，该图是$（n-3）$ - 仅沿适当的实际子变量退化，不等于多项式图。特别是，通过更改基点，可以构建新的非等级图的新家庭。
For $N \geq 4$ we classify the $(N-3)$-degenerate smooth CR maps of the three-dimensional unit sphere into the $(2N-1)$-dimensional unit sphere. Each of these maps has image being contained in a five-dimensional complex-linear space and is of degree at most two, or equivalent to one of the four maps into the five-dimensional sphere classified by Faran. As a byproduct of our classification we obtain new examples of rational maps of degree three which are $(N-3)$-degenerate only along a proper real subvariety and are not equivalent to polynomial maps. In particular, by changing the base point, it is possible to construct new families of nondegenerate maps.
