Distance squared 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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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914895400796160 |
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| author | Fukui, Toshizumi Hasegawa, Masaru |
| author_facet | Fukui, Toshizumi Hasegawa, Masaru |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distance squared functions on singular surfaces parameterized by smooth maps $\mathcal{A}$-equivalent to $S_k$, $B_k$, $C_k$ and $F_4$ Fukui, Toshizumi Hasegawa, Masaru Differential Geometry 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. |
| title | Distance squared functions on singular surfaces parameterized by smooth maps $\mathcal{A}$-equivalent to $S_k$, $B_k$, $C_k$ and $F_4$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2408.00231 |