Vol. 11, No. 1, 2010

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Generalized Clifford parallelisms

Andrea Blunck, Stefano Pasotti and Silvia Pianta

Vol. 11 (2010), No. 1, 197–212
DOI: 10.2140/iig.2010.11.197
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.

Keywords
Clifford parallelism, quadratic forms, quadrics, quaternions
Mathematical Subject Classification 2010
Primary: 11E04, 51A15, 51J15
Milestones
Received: 11 December 2008
Accepted: 15 May 2010
Authors
Andrea Blunck
Stefano Pasotti
Silvia Pianta