Aequationes mathematicae

, Volume 92, Issue 2, pp 385–400 | Cite as

Geometry on the lines of spine spaces

  • Krzysztof Petelczyc
  • Mariusz Żynel
Open Access


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.


Grassmann space Projective space Spine space Coplanarity 

Mathematics Subject Classification

51A15 51A45 


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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of BiałystokBiałystokPoland

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