Clifford-like parallelisms

Abstract

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 $(\mathbb{P},{\parallel }_{\ell },{\parallel }_r)$ over a quaternion skew field we characterise the "Clifford-like" parallelisms, i.e. the blends of the Clifford parallelisms ${\parallel }_{\ell }$ and ${\parallel }_r$, 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.

Dedicated to Helmut Karzel on the occasion of his 90th birthday

References in corpus (3)

• A note on Clifford parallelisms in characteristic two
• Clifford Parallelisms and External Planes to the Klein quadric
• Pencilled regular parallelisms

Cited by in corpus (2)

• Characterising Clifford parallelisms among Clifford-like parallelisms
• Automorphisms of a Clifford-like parallelism