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 \(({\mathbb P},{\mathrel {\parallel _{\ell }}},{\mathrel {\parallel _{r}}})\) over a quaternion skew field we characterise the “Clifford-like” parallelisms, i.e. the blends of the Clifford parallelisms \(\mathrel {\parallel _{\ell }}\) and \(\mathrel {\parallel _{r}}\), 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.
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Dedicated to Helmut Karzel on the occasion of his 90th birthday.
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This work was partially supported by GNSAGA of INdAM (Italy) and the International Office of TU Wien (Austria). The authors acknowledge the TU Wien University Library for financial support through its Open Access Funding Programme.
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Havlicek, H., Pasotti, S. & Pianta, S. Clifford-like parallelisms. J. Geom. 110, 2 (2019). https://doi.org/10.1007/s00022-018-0456-9
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DOI: https://doi.org/10.1007/s00022-018-0456-9