Coplanarity of lines in projective and polar Grassmann spaces

DOI10.1007/s00010-015-0387-6zbMath1351.51005OpenAlexW2284811569WikidataQ59472231 ScholiaQ59472231MaRDI QIDQ291296

Mariusz Żynel, Krzysztof Petelczyc

Publication date: 7 June 2016

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-015-0387-6

zbMATH Keywords

projective spacepolar spacebundle spacecoplanarityGrassmann space

Mathematics Subject Classification ID

Incidence structures embeddable into projective geometries (51A45) Polar geometry, symplectic spaces, orthogonal spaces (51A50)

Related Items

Geometry on the lines of spine spaces ⋮ Geometry on the lines of polar spine spaces

Cites Work

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• A characteristic property of elliptic Plücker transformations
• Bestimmung der orthogonalitätstreuen Permutationen Euklidischer Räume. (Determination of orthogonality preserving permutations of Euclidean spaces)
• Eine Kennzeichnung der Ähnlichkeiten affiner Räume mit definiter Orthogonalitätsstruktur. (A characterization of similarities of affine spaces with definite orthogonality structure)
• Locally projective-planar lattices which satisfy the bundle theorem
• The undefinability of intersection from perpendicularity in the three- dimensional Euclidean geometry of lines
• Locally generalized projective lattices satisfying a bundle theorem
• Construction of hyperbolic geometry from the notion of line orthogonality
• On the axiomatics of projective and affine geometry in terms of line intersection
• Locally projective spaces which satisfy the bundle theorem
• Defining co-punctuality in terms of line-orthogonality in plane hyperbolic geometry
• Possible primitive notions for geometry of spine spaces
• Zur Begründung der projektiven Geometrie: Einführung idealer Elemente unabhängig von der Anordnung
• On the geometry of algebraic homogeneous spaces
• Orthogonality of subspaces in metric-projective geometry
• GEOMETRY OF POLAR GRASSMANN SPACES
• Grassmannians of Classical Buildings
• Relations on lines as primitive notions for Euclidean geometry
• Isomorphisms of Affine Pl\"ucker Spaces
• An Axiomatics for Hyperbolic Projective-Metric Planes in Terms of Lines and Orthogonality
• An Axiomatic Line Geometry
• Harmonic mappings and hyperbolic Plücker transformations
• On orthogonality-preserving Plücker transformations of hyperbolic spaces