Shapes of surfaces that contain a great and a small circle through each point
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866915626150264832 |
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| author | Lubbes, Niels |
| author_facet | Lubbes, Niels |
| contents | We classify the topological types of surfaces in the 3-dimensional unit sphere that contain both a great and a small circle through each point. In particular, these surfaces are homeomorphic to one of five normal forms and are either the pointwise product of circles in the unit quaternions or contain five concurrent circles. We classify the real singular loci of such surfaces and characterize how circles in the surface meet the self-intersection locus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_14438 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Shapes of surfaces that contain a great and a small circle through each point Lubbes, Niels Algebraic Geometry Geometric Topology 51B10, 51M15, 14J17, 14P25 We classify the topological types of surfaces in the 3-dimensional unit sphere that contain both a great and a small circle through each point. In particular, these surfaces are homeomorphic to one of five normal forms and are either the pointwise product of circles in the unit quaternions or contain five concurrent circles. We classify the real singular loci of such surfaces and characterize how circles in the surface meet the self-intersection locus. |
| title | Shapes of surfaces that contain a great and a small circle through each point |
| topic | Algebraic Geometry Geometric Topology 51B10, 51M15, 14J17, 14P25 |
| url | https://arxiv.org/abs/2205.14438 |