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,∥) over a quaternion skew field we characterise the “Clifford-like” parallelisms, i.e. the blends of the Clifford parallelisms ∥ℓ and ∥, 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.
Clifford-like parallelisms
Pasotti, Stefano;
2019-01-01
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,∥) over a quaternion skew field we characterise the “Clifford-like” parallelisms, i.e. the blends of the Clifford parallelisms ∥ℓ and ∥, 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.File in questo prodotto:
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