Equiaffine structure on frontals
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866915138957737984 |
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| author | Santos, Igor Chagas |
| author_facet | Santos, Igor Chagas |
| contents | In this paper, we generalize the idea of equiaffine structure to the case of frontals and we define the Blaschke vector field of a frontal. We also investigate some necessary and sufficient conditions that a frontal needs to satisfy to have a Blaschke vector field and provide some examples. Finally, taking the theory developed here into account we present a fundamental theorem, which is a version for frontals of the fundamental theorem of affine differential geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_10847 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Equiaffine structure on frontals Santos, Igor Chagas Differential Geometry 53A15, 53A05, 57R45 In this paper, we generalize the idea of equiaffine structure to the case of frontals and we define the Blaschke vector field of a frontal. We also investigate some necessary and sufficient conditions that a frontal needs to satisfy to have a Blaschke vector field and provide some examples. Finally, taking the theory developed here into account we present a fundamental theorem, which is a version for frontals of the fundamental theorem of affine differential geometry. |
| title | Equiaffine structure on frontals |
| topic | Differential Geometry 53A15, 53A05, 57R45 |
| url | https://arxiv.org/abs/2210.10847 |