Orthogonality of subspaces in metric-projective geometry

In an n-dimensional projective space with a polarity two k-subspaces are ortho-adjacent if they are adjacent and one intersects the polar of the other. We prove that this relation on the set of all non-isotropic k-subspaces can be used as a single primitive notion for metric-projective geometry prov...

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Bibliographic Details
Published inAdvances in geometry Vol. 11; no. 1; pp. 103 - 116
Main Authors Prażmowski, Krzysztof, Żynel, Mariusz
Format Journal Article
LanguageEnglish
Published Walter de Gruyter GmbH & Co. KG 01.01.2011
Subjects
adjacency
elliptic space
hyperbolic space
Metric-projective space
ortho-adjacency
orthogonality
polarity
symplectic space
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Summary:In an n-dimensional projective space with a polarity two k-subspaces are ortho-adjacent if they are adjacent and one intersects the polar of the other. We prove that this relation on the set of all non-isotropic k-subspaces can be used as a single primitive notion for metric-projective geometry provided that the polarity is not symplectic and n ≠ 2k + 1.
Bibliography:advgeom.2010.041.pdf
ark:/67375/QT4-Q0L8L8XM-3
ArticleID:advg.11.1.103
istex:3686497DEC8E93262444C87111E75187D8FB1AAE
ISSN:1615-715X
1615-7168
DOI:10.1515/advgeom.2010.041