Débora Lopes, Tito Alexandro Medina Tejeda, Maria Aparecida Soares Ruas, Igor Chagas Santos
Published 2022-10-25Version 1
This paper is a first step in order to extend Kummer's theory for line congruences to the case $\lbrace x, \xi \rbrace $, where $x: U \rightarrow \mathbb{R}^3$ is a smooth map and $\xi: U \rightarrow \mathbb{R}^3$ is a proper frontal. We show that if $\lbrace x, \xi \rbrace$ 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 $\xi$.
Singularities of 3-parameter line congruences in $\mathbb{R}^4$
The fundamental theorem for singular surfaces with limiting tangent planes
Height functions on singular surfaces parameterized by smooth maps $\mathcal{A}$-equivalent to $S_k$, $B_k$, $C_k$ and $F_4$
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