仿射等距点的奇性：四维空间中曲面的外几何
Singularities of affine equidistants: extrinsic geometry of surfaces in 4-space
摘要：
对于光滑闭曲面$M$到$\mathbb R^4$的一般嵌入，$\mathbb R^4$的仿射$λ$ -等距的子集表现为稳定映射$M \times M \to \mathbb R^4$的判别集，因此它们的稳定奇点是$A_k, \, k=2, 3, 4,$和$C_{2,2}^{\pm}$。在本文中，我们描述了这些稳定的奇异性$λ$等距的双局部外在几何的表面，导致几何研究的一组弱平行点的$M$。
英文摘要：
For a generic embedding of a smooth closed surface $M$ into $\mathbb R^4$, the subset of $\mathbb R^4$ which is the affine $λ$-equidistant of $M$ appears as the discriminant set of a stable mapping $M \times M \to \mathbb R^4$, hence their stable singularities are $A_k, \, k=2, 3, 4,$ and $C_{2,2}^{\pm}$. In this paper, we characterize these stable singularities of $λ$-equidistants in terms of the bi-local extrinsic geometry of the surface, leading to a geometrical study of the set of weakly parallel points on $M$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
