Geometry of the parallelism in polar spine spaces and their line reducts
| Autor: | Krzysztof Prażmowski, Krzysztof Petelczyc, Mariusz Żynel |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Parallelism (rhetoric) Quantitative Biology::Tissues and Organs 010102 general mathematics Geometry 0102 computer and information sciences Coplanarity Space (mathematics) 01 natural sciences Theoretical Computer Science Combinatorics 010201 computation theory & mathematics Line (geometry) Discrete Mathematics and Combinatorics Polar Projective space Geometry and Topology Affine transformation 0101 mathematics Polar space Mathematics |
| Zdroj: | Ars Mathematica Contemporanea. 20:151-170 |
| ISSN: | 1855-3974 1855-3966 |
| DOI: | 10.26493/1855-3974.2201.b65 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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