Geometry on the lines of spine spaces

Spine spaces can be considered as fragments of a projective Grassmann space. We prove that the structure of lines together with a binary coplanarity relation, as well as with the binary relation of being in one pencil of lines, is a sufficient system of primitive notions for these geometries. It is...

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Bibliographic Details
Published inAequationes mathematicae Vol. 92; no. 2; pp. 385 - 400
Main Authors Petelczyc, Krzysztof, Żynel, Mariusz
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.04.2018
Subjects
Analysis
Combinatorics
Mathematics
Mathematics and Statistics
Coplanarity
Spine space
Grassmann space
51A15
51A45
Projective space
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Summary:Spine spaces can be considered as fragments of a projective Grassmann space. We prove that the structure of lines together with a binary coplanarity relation, as well as with the binary relation of being in one pencil of lines, is a sufficient system of primitive notions for these geometries. It is also shown that, over a spine space, the geometry of pencils of lines can be reconstructed in terms of the two binary relations.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-017-0523-6