论文标题
在以纯正额定点的正常额叶一致性的奇异基因座获得的表面上
On surfaces obtained as singular loci of normal congruences of frontals with pure-frontal singular points
论文作者
论文摘要
我们研究表面的奇异性和几何特性，由具有纯粹额外奇异点的正常一致性的奇异基因座给出。这些表面由最初额叶的正常排除表面和局灶性表面组成。对于正常统治的表面，我们从奇异点集中定义的初始额叶的几何不变的角度给出了奇异性的特征。对于焦点表面，我们显示它们的某些奇异性与给定额叶的几何特性之间的关系。此外，我们考虑了额叶边缘的额叶局灶性表面高斯曲率的行为。
We study singularities and geometric properties of surfaces given by the singular loci of normal congruence of frontals with pure-frontal singular points. These surfaces consist of the normal ruled surface and focal surfaces of the initial frontal. For the normal ruled surface, we give characterizations of singularities in terms of geometric invariants of the initial frontal defined on the set of singular points. For focal surfaces, we show relation between certain singularities of them and geometric property of the given frontal. Moreover, we consider behavior of Gaussian curvature of focal surfaces of frontal with a $5/2$-cuspidal edge.
