论文标题
线的一致性奇异表面
Line Congruences on singular surfaces
论文作者
论文摘要
本文是将Kummer的理论扩展到case $ \ lbrace x，ξ\ rbrace $的第一步，其中$ x：u \ rightarrow \ mathbb {r}^3 $是平滑的地图和$ξ：u \ rightarrow \ rightArrow \ rightArrow \ rightArrow \ m athbb {r}^3 $是适当的frontal。我们表明，如果$ \ lbrace x，ξ\ rbrace $是正常的一致性，则主表面的方程是可开发表面方程的倍数，此外，乘法因子与$ξ$的单数集有关。
This paper is a first step in order to extend Kummer's theory for line congruences to the case $\lbrace x, ξ\rbrace $, where $x: U \rightarrow \mathbb{R}^3$ is a smooth map and $ξ: U \rightarrow \mathbb{R}^3$ is a proper frontal. We show that if $\lbrace x, ξ\rbrace$ is a normal congruence, the equation of the principal surfaces is a multiple of the equation of the developable surfaces, furthermore, the multiplicative factor is associated to the singular set of $ξ$.
