Geometric deformations of cuspidal $S_1$ singularities
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909503542263808 |
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| author | Shimada, Runa |
| author_facet | Shimada, Runa |
| contents | To study a deformation of a singularity taking into consideration their differential geometric properties, a form representing the deformation using only diffeomorphisms on the source space and isometries of the target space plays a crucial role. Such a form for an $S_1$ singularity is obtained by the author's previous work. On this form, we give a necessary and sufficient condition for such a map is being a frontal. The form for an $S_1$ singularity with the frontal condition can be considered such a form for a cuspidal $S_1$ singularity. Using this form, we investigate geometric properties of cuspidal $S_1$ singularities and the cuspidal cross caps appearing in the deformation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15328 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric deformations of cuspidal $S_1$ singularities Shimada, Runa Differential Geometry 57R45, 53A05 To study a deformation of a singularity taking into consideration their differential geometric properties, a form representing the deformation using only diffeomorphisms on the source space and isometries of the target space plays a crucial role. Such a form for an $S_1$ singularity is obtained by the author's previous work. On this form, we give a necessary and sufficient condition for such a map is being a frontal. The form for an $S_1$ singularity with the frontal condition can be considered such a form for a cuspidal $S_1$ singularity. Using this form, we investigate geometric properties of cuspidal $S_1$ singularities and the cuspidal cross caps appearing in the deformation. |
| title | Geometric deformations of cuspidal $S_1$ singularities |
| topic | Differential Geometry 57R45, 53A05 |
| url | https://arxiv.org/abs/2502.15328 |