Geometry of the parallelism in polar spine spaces and their line reducts

Krzysztof Petelczyc, Krzysztof Prażmowski, Mariusz Żynel

Abstract


The concept of the spine geometry over a polar Grassmann space belongs to a wide family of partial affine line spaces. It is known that the geometry of a spine space over a projective Grassmann space can be developed in terms of points, so called affine lines, and their parallelism (in this case the parallelism is not intrinsically definable as it is not Veblenian). This paper aims to prove an analogous result for the polar spine spaces. As a by-product we obtain several other results on primitive notions for the geometry of polar spine spaces.

Keywords


Grassmann space, projective space, polar space, spine space, coplanarity, pencil of lines

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DOI: https://doi.org/10.26493/1855-3974.2201.b65

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications