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Please use this identifier to cite or link to this item: https://doi.org/10.21256/zhaw-1746
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dc.contributor.authorBödi, Richard-
dc.date.accessioned2018-02-27T15:15:19Z-
dc.date.available2018-02-27T15:15:19Z-
dc.date.issued1997-05-
dc.identifier.issn1420-9012de_CH
dc.identifier.issn1422-6383de_CH
dc.identifier.urihttps://digitalcollection.zhaw.ch/handle/11475/3267-
dc.descriptionErworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)de_CH
dc.description.abstractThis paper deals with smooth stable planes which generalize the notion of differentiable (affine or projective) planes. It is intended to be the first one of a series of papers on smooth incidence geometry based on the Habilitationsschrift of the author. It contains the basic definitions and results which are needed to build up a foundation for a systematic study of smooth planes. We define smooth stable planes, and we prove that point rows and line pencils are closed submanifolds of the point set and line set, respectively (Theorem (1.6)). Moreover, the flag space is a closed submanifold of the product manifold P×L (Theorem (1.14)), and the smooth structure on the set P of points and on the set L of lines is uniquely determined by the smooth structure of one single line pencil. In the second section it is shown that for any point p \te P the tangent space TpP carries the structure of a locally compact affine translation plane A p , see Theorem (2.5). Dually, we prove in Section 3 that for any line L∈L the tangent space T L L together with the set S L ={T L L p ∣p∈L} gives rise to some shear plane. It turned out that the translation planes A p are one of the most important tools in the investigation of smooth incidence geometries. The linearization theorems (3.9), (3.11), and (4.4) can be viewed as the main results of this paper. In the closing section we investigate some homogeneity properties of smooth projective planes.de_CH
dc.language.isoende_CH
dc.publisherSpringerde_CH
dc.relation.ispartofResults in Mathematicsde_CH
dc.rightsLicence according to publishing contractde_CH
dc.subjectStable planede_CH
dc.subjectSmoothde_CH
dc.subjectDifferentiable incidence geometryde_CH
dc.subjectTangent translation planede_CH
dc.subject.ddc510: Mathematikde_CH
dc.titleSmooth stable planesde_CH
dc.typeBeitrag in wissenschaftlicher Zeitschriftde_CH
dcterms.typeTextde_CH
zhaw.departementSchool of Engineeringde_CH
zhaw.publisher.placeBaselde_CH
dc.identifier.doi10.21256/zhaw-1746-
dc.identifier.doi10.1007/BF03322167de_CH
zhaw.funding.euNode_CH
zhaw.issue3-4de_CH
zhaw.originated.zhawYesde_CH
zhaw.pages.end321de_CH
zhaw.pages.start300de_CH
zhaw.publication.statuspublishedVersionde_CH
zhaw.volume31de_CH
zhaw.publication.reviewPeer review (Publikation)de_CH
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Bödi, R. (1997). Smooth stable planes. Results in Mathematics, 31(3-4), 300–321. https://doi.org/10.21256/zhaw-1746
Bödi, R. (1997) ‘Smooth stable planes’, Results in Mathematics, 31(3-4), pp. 300–321. Available at: https://doi.org/10.21256/zhaw-1746.
R. Bödi, “Smooth stable planes,” Results in Mathematics, vol. 31, no. 3-4, pp. 300–321, May 1997, doi: 10.21256/zhaw-1746.
BÖDI, Richard, 1997. Smooth stable planes. Results in Mathematics. Mai 1997. Bd. 31, Nr. 3-4, S. 300–321. DOI 10.21256/zhaw-1746
Bödi, Richard. 1997. “Smooth Stable Planes.” Results in Mathematics 31 (3-4): 300–321. https://doi.org/10.21256/zhaw-1746.
Bödi, Richard. “Smooth Stable Planes.” Results in Mathematics, vol. 31, no. 3-4, May 1997, pp. 300–21, https://doi.org/10.21256/zhaw-1746.


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