Innovations in Incidence Geometry

Generalized Clifford parallelisms

Andrea Blunck, Stefano Pasotti, and Silvia Pianta

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Abstract

We define generalized Clifford parallelisms in PG ( 3 , F ) with the help of a quaternion skew field H over a field F of arbitrary characteristic. Moreover we give a geometric description of such parallelisms involving hyperbolic quadrics in projective spaces over suitable quadratic extensions of F .

Article information

Source
Innov. Incidence Geom., Volume 11, Number 1 (2010), 197-212.

Dates
Received: 11 December 2008
Accepted: 15 May 2010
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323090

Digital Object Identifier
doi:10.2140/iig.2010.11.197

Mathematical Reviews number (MathSciNet)
MR2795063

Zentralblatt MATH identifier
1260.51001

Subjects
Primary: 11E04: Quadratic forms over general fields 51A15: Structures with parallelism 51J15: Kinematic spaces

Keywords
Clifford parallelism quadratic forms quadrics quaternions

Citation

Blunck, Andrea; Pasotti, Stefano; Pianta, Silvia. Generalized Clifford parallelisms. Innov. Incidence Geom. 11 (2010), no. 1, 197--212. doi:10.2140/iig.2010.11.197. https://projecteuclid.org/euclid.iig/1551323090


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