Translational and great Darboux cyclides
A surface that is the pointwise sum of circles in Euclidean space is either coplanar or contains no more than 2 circles through a general point. A surface that is the pointwise product of circles in the unit-quaternions contains either 2, 3, 4, or 5 circles through a general point. A surface in a un...
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.603/ |
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| author | Lubbes, Niels |
| author_facet | Lubbes, Niels |
| author_sort | Lubbes, Niels |
| collection | DOAJ |
| description | A surface that is the pointwise sum of circles in Euclidean space is either coplanar or contains no more than 2 circles through a general point. A surface that is the pointwise product of circles in the unit-quaternions contains either 2, 3, 4, or 5 circles through a general point. A surface in a unit-sphere of any dimension that contains 2 great circles through a general point contains either 4, 5, 6, or infinitely many circles through a general point. These are some corollaries from our classification of translational and great Darboux cyclides. We use the combinatorics associated to the set of low degree curves on such surfaces modulo numerical equivalence. |
| format | Article |
| id | doaj-art-183c87c88f6d4706a3ce8c1e7844642a |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-183c87c88f6d4706a3ce8c1e7844642a2025-02-07T11:20:51ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G441344810.5802/crmath.60310.5802/crmath.603Translational and great Darboux cyclidesLubbes, Niels0Institute for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, AustriaA surface that is the pointwise sum of circles in Euclidean space is either coplanar or contains no more than 2 circles through a general point. A surface that is the pointwise product of circles in the unit-quaternions contains either 2, 3, 4, or 5 circles through a general point. A surface in a unit-sphere of any dimension that contains 2 great circles through a general point contains either 4, 5, 6, or infinitely many circles through a general point. These are some corollaries from our classification of translational and great Darboux cyclides. We use the combinatorics associated to the set of low degree curves on such surfaces modulo numerical equivalence.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.603/real surfacespencils of circlessingular locusDarboux cyclidesClifford torusMöbius geometryelliptic geometryhyperbolic geometryEuclidean geometryEuclidean translationsClifford translationsunit quaternionsweak del Pezzo surfacesdivisor classesNéron–Severi lattice |
| spellingShingle | Lubbes, Niels Translational and great Darboux cyclides Comptes Rendus. Mathématique real surfaces pencils of circles singular locus Darboux cyclides Clifford torus Möbius geometry elliptic geometry hyperbolic geometry Euclidean geometry Euclidean translations Clifford translations unit quaternions weak del Pezzo surfaces divisor classes Néron–Severi lattice |
| title | Translational and great Darboux cyclides |
| title_full | Translational and great Darboux cyclides |
| title_fullStr | Translational and great Darboux cyclides |
| title_full_unstemmed | Translational and great Darboux cyclides |
| title_short | Translational and great Darboux cyclides |
| title_sort | translational and great darboux cyclides |
| topic | real surfaces pencils of circles singular locus Darboux cyclides Clifford torus Möbius geometry elliptic geometry hyperbolic geometry Euclidean geometry Euclidean translations Clifford translations unit quaternions weak del Pezzo surfaces divisor classes Néron–Severi lattice |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.603/ |
| work_keys_str_mv | AT lubbesniels translationalandgreatdarbouxcyclides |