Geometry on the lines of polar spine spaces

The concept of spine geometry over a polar Grassmann space is introduced. We determine conditions under which the structure of lines together with a binary coplanarity relation is a sufficient system of primitive notions for polar spine spaces. These assumptions also allow to characterize polar spin...

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Bibliographic Details
Published in:Aequationes mathematicae 2020-10, Vol.94 (5), p.829-846
Main Authors: Petelczyc, Krzysztof, Prażmowski, Krzysztof, Żynel, Mariusz
Format: Article
Language:English
Subjects:
Analysis
Combinatorics
Coplanarity
Mathematics
Mathematics and Statistics
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Summary:The concept of spine geometry over a polar Grassmann space is introduced. We determine conditions under which the structure of lines together with a binary coplanarity relation is a sufficient system of primitive notions for polar spine spaces. These assumptions also allow to characterize polar spine spaces in terms of the binary relation of being in one pencil of lines.
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-020-00733-2