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.
Havlicek, H., Pasotti, S., Pianta, S., Clifford-like parallelisms, <<JOURNAL OF GEOMETRY>>, 2019; 110 (1): 1-18. [doi:10.1007/s00022-018-0456-9] [http://hdl.handle.net/10807/129192]
Clifford-like parallelisms
Pianta, Silvia
2019
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 (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.
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