Clifford-like parallelisms

Given two parallelisms of a projective space we describe a construction, called blending, that yields a (possibly new) parallelism of this space. For a projective double space ( P , ‖ ℓ , ‖ r ) over a quaternion skew field we characterise the “Clifford-like” parallelisms, i.e. the blends of the Clif...

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Bibliographic Details
Published in:	Journal of geometry Vol. 110; no. 1; pp. 1 - 18
Main Authors:	Havlicek, Hans, Pasotti, Stefano, Pianta, Silvia
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-04-2019 Springer Nature B.V
Subjects:	Geometry Karzel Anniversary Topical Collection Mathematics Mathematics and Statistics Quaternions quaternion skew field 51J15 Clifford parallelism projective double space 51A15 Blend of parallelisms
Online Access:	Get full text
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Summary:	Given two parallelisms of a projective space we describe a construction, called blending, that yields a (possibly new) parallelism of this space. For a projective double space ( P , ‖ ℓ , ‖ r ) over a quaternion skew field we characterise the “Clifford-like” parallelisms, i.e. the blends of the Clifford parallelisms ‖ ℓ and ‖ r , in a geometric and an algebraic way. Finally, we establish necessary and sufficient conditions for the existence of Clifford-like parallelisms that are not Clifford.
ISSN:	0047-2468 1420-8997
DOI:	10.1007/s00022-018-0456-9