Stable umbilical points of a W-congruence
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908732198223872 |
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| author | Craizer, Marcos Garcia, Ronaldo Alves |
| author_facet | Craizer, Marcos Garcia, Ronaldo Alves |
| contents | The class of $W$-congruences is a central object of Projective Differential Geometry. Nevertheless, their singularities has not been extensively studied. In this paper we prove a characterization of $W$-congruences that allow us to study their umbilical points. We describe examples of isolated stable umbilical points of type $A_m$, $m\in\{1,2,3,4\}$, and discuss some partial results concerning the generalization of these results to any $m\in\mathbb{N}\cup\{\infty\}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07289 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stable umbilical points of a W-congruence Craizer, Marcos Garcia, Ronaldo Alves Differential Geometry 53A20, 53A25 The class of $W$-congruences is a central object of Projective Differential Geometry. Nevertheless, their singularities has not been extensively studied. In this paper we prove a characterization of $W$-congruences that allow us to study their umbilical points. We describe examples of isolated stable umbilical points of type $A_m$, $m\in\{1,2,3,4\}$, and discuss some partial results concerning the generalization of these results to any $m\in\mathbb{N}\cup\{\infty\}$. |
| title | Stable umbilical points of a W-congruence |
| topic | Differential Geometry 53A20, 53A25 |
| url | https://arxiv.org/abs/2504.07289 |