Geometric deformations of cuspidal $S_1$ singularities

Runa Shimada

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arXiv · 2502.15328

Geometric deformations of cuspidal $S_1$ singularities

Runa Shimada

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Abstract

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.

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BibTeX RIS

Runa Shimada. 2025-02-21. Geometric deformations of cuspidal $S_1$ singularities. https://arxiv.org/abs/2502.15328

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