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 binary coplanarity relation, as well as with binary relation of being in one pencil of lines, is a sufficient system of primitive notions for these geometries. It is also s...

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Bibliographic Details
Published in:arXiv.org 2017-04
Main Authors: Petelczyc, K, Żynel, M
Format: Article
Language:English
Subjects:
Coplanarity
Online Access:Get full text
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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 binary coplanarity relation, as well as with 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:2331-8422