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https://doi.org/10.21256/zhaw-1743Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Bödi, Richard | - |
| dc.date.accessioned | 2018-02-27T15:02:52Z | - |
| dc.date.available | 2018-02-27T15:02:52Z | - |
| dc.date.issued | 1998-11-01 | - |
| dc.identifier.issn | 0933-7741 | de_CH |
| dc.identifier.uri | https://digitalcollection.zhaw.ch/handle/11475/3260 | - |
| dc.description | Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch) | de_CH |
| dc.description.abstract | Smooth stable planes have been introduced in [4]. We show that every continuous collineation between two smooth stable planes is in fact a smooth collineation. This implies that the group Γ of all continuous collineations of a smooth stable plane is a Lie transformation group on both the set P of points and the set ℒ of lines. In particular, this shows that the point and line sets of a (topological) stable plane ℐ admit at most one smooth structure such that ℐ becomes a smooth stable plane. The investigation of central and axial collineations in the case of (topological) stable planes due to R. Löwen ([25], [26], [27]) is continued for smooth stable planes. Many results of [26] which are only proved for low dimensional planes (dim ℐ ≤ 4) are transferred to smooth stable planes of arbitrary finite dimension. As an application of these transfers we show that the stabilizers Γ[c,c] 1 and Γ[A,A] 1 (see (3.2) Notation) are closed, simply connected, solvable subgroups of Aut(ℐ) (Corollary (4.17)). Moreover, we show that Γ[c,c] is even abelian (Theorem (4.18)). In the closing section we investigate the behaviour of reflections. | de_CH |
| dc.language.iso | en | de_CH |
| dc.publisher | De Gruyter | de_CH |
| dc.relation.ispartof | Forum Mathematicum | de_CH |
| dc.rights | Licence according to publishing contract | de_CH |
| dc.subject.ddc | 510: Mathematik | de_CH |
| dc.title | Collineations of smooth stable planes | de_CH |
| dc.type | Beitrag in wissenschaftlicher Zeitschrift | de_CH |
| dcterms.type | Text | de_CH |
| zhaw.departement | School of Engineering | de_CH |
| zhaw.publisher.place | de Gruyter | de_CH |
| dc.identifier.doi | 10.21256/zhaw-1743 | - |
| dc.identifier.doi | 10.1515/form.10.6.751 | de_CH |
| zhaw.funding.eu | No | de_CH |
| zhaw.issue | 6 | de_CH |
| zhaw.originated.zhaw | Yes | de_CH |
| zhaw.pages.end | 773 | de_CH |
| zhaw.pages.start | 751 | de_CH |
| zhaw.publication.status | publishedVersion | de_CH |
| zhaw.volume | 10 | de_CH |
| zhaw.publication.review | Peer review (Publikation) | de_CH |
| Appears in collections: | Publikationen School of Engineering | |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| 1998_Bödi_Collineations of smooth stable planes_Forum Math.pdf | 1.85 MB | Adobe PDF |  View/Open |
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Bödi, R. (1998). Collineations of smooth stable planes. Forum Mathematicum, 10(6), 751–773. https://doi.org/10.21256/zhaw-1743
Bödi, R. (1998) ‘Collineations of smooth stable planes’, Forum Mathematicum, 10(6), pp. 751–773. Available at: https://doi.org/10.21256/zhaw-1743.
R. Bödi, “Collineations of smooth stable planes,” Forum Mathematicum, vol. 10, no. 6, pp. 751–773, Nov. 1998, doi: 10.21256/zhaw-1743.
BÖDI, Richard, 1998. Collineations of smooth stable planes. Forum Mathematicum. 1 November 1998. Bd. 10, Nr. 6, S. 751–773. DOI 10.21256/zhaw-1743
Bödi, Richard. 1998. “Collineations of Smooth Stable Planes.” Forum Mathematicum 10 (6): 751–73. https://doi.org/10.21256/zhaw-1743.
Bödi, Richard. “Collineations of Smooth Stable Planes.” Forum Mathematicum, vol. 10, no. 6, Nov. 1998, pp. 751–73, https://doi.org/10.21256/zhaw-1743.
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