A geometric construction of generalized quadrangles from polar spaces of rank three

DOI10.1007/BF03323091zbMath0765.51006MaRDI QIDQ1193234

Norbert Knarr

Publication date: 27 September 1992

Published in: Results in Mathematics (Search for Journal in Brave)

zbMATH Keywords

generalized quadranglespolar spaces of rank three

Mathematics Subject Classification ID

Generalized quadrangles and generalized polygons in finite geometry (51E12) Polar geometry, symplectic spaces, orthogonal spaces (51A50)

Related Items (21)

Spreads and ovoids in finite generalized quadrangles ⋮ Classification of flocks of the quadratic cone in PG(3,64) ⋮ On the geometry of regular hyperbolic fibrations ⋮ Automorphism groups of generalized quadrangles via an unusual action of \(P\Gamma L (2,2^h)\) ⋮ The uniqueness of 1-systems of \(W_5(q)\) satisfying the BLT-property, with \(q\) odd ⋮ Subquadrangles of order \(s\) of generalized quadrangles of order \((s,s^{2})\). III ⋮ Some remarks on flocks ⋮ ELATION GENERALIZED QUADRANGLES FOR WHICH THE NUMBER OF LINES ON A POINT IS THE SUCCESSOR OF A PRIME ⋮ Flocks of cones of higher degree ⋮ On \(q\)-clans in even characteristic ⋮ Hemisystems of small flock generalized quadrangles ⋮ The pseudo-hyperplanes and homogeneous pseudo-embeddings of the generalized quadrangles of order \((3,t)\) ⋮ Construction of BLT-sets over small fields. ⋮ Geometrical constructions of flock generalized quadrangles ⋮ Some flocks in characteristic 3 ⋮ On monomial flocks ⋮ SPG-reguli, SPG-systems, BLT-sets and sets with the BLT-property ⋮ Special sets of the Hermitian surface and indicator sets ⋮ Subquadrangles of order \(s\) of generalized quadrangles of order (\(s,s^{2}\)). II ⋮ Generalized quadrangles of order \((s,s^2)\). III ⋮ Flock generalized quadrangles and tetradic sets of elliptic quadrics of PG\((3,q)\)

Cites Work

• On the foundations of polar geometry. II
• Generalized quadrangles and flocks of cones
• Flocks of quadratic cones, generalized quadrangles and translation planes
• Spreads, flocks, and generalized quadrangles
• Generalized quadrangles associated with \(G_ 2(\)q)
• Generalized quadrangles, flocks, and BLT sets
• Buildings of spherical type and finite BN-pairs
• Representation and construction of projective planes and other geometric structures from projective spaces
• Endliche translationstransitive postaffine Räume
• Polar spaces of arbitrary rank
• On the foundations of polar geometry
• Derivation of Flocks of Quadratic Cones
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