TY - JOUR
T1 - Clifford-like parallelisms
AU - Havlicek, Hans
AU - Pasotti, Stefano
AU - Pianta, Silvia
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - Blend of parallelisms
KW - Clifford parallelism
KW - projective double space
KW - quaternion skew field
KW - Blend of parallelisms
KW - Clifford parallelism
KW - projective double space
KW - quaternion skew field
UR - http://hdl.handle.net/10807/129192
UR - https://link.springer.com/journal/22
U2 - 10.1007/s00022-018-0456-9
DO - 10.1007/s00022-018-0456-9
M3 - Article
SN - 0047-2468
VL - 110
SP - 1
EP - 18
JO - Journal of Geometry
JF - Journal of Geometry
ER -