Distance squared functions on singular surfaces parameterized by smooth maps $\mathcal{A}$-equivalent to $S_k$, $B_k$, $C_k$ and $F_4$

Toshizumi Fukui; Masaru Hasegawa

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arXiv · 2408.00231

Distance squared functions on singular surfaces parameterized by smooth maps $\mathcal{A}$-equivalent to $S_k$, $B_k$, $C_k$ and $F_4$

Toshizumi Fukui·Masaru Hasegawa

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Abstract

We describe singularities of distance squared functions on singular surfaces in $\mathbb{R}^3$ parameterized by smooth map-germs $\mathcal{A}$-equivalent to one of $S_k$, $B_k$, $C_k$ and $F_4$ singularities in terms of extended geometric language via finite succession of blowing-ups. We investigate singularities of wave-fronts and caustics of such singular surfaces.

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Toshizumi Fukui, Masaru Hasegawa. 2024-08-01. Distance squared functions on singular surfaces parameterized by smooth maps $\mathcal{A}$-equivalent to $S_k$, $B_k$, $C_k$ and $F_4$. https://arxiv.org/abs/2408.00231

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