Characterising Clifford parallelisms among Clifford-like parallelisms

• Published in: Beiträge zur Algebra und Geometrie Vol. 62; no. 1; pp. 37 - 54
• Main Authors: Havlicek, Hans, Pasotti, Stefano, Pianta, Silvia
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-03-2021; Springer Nature B.V
• Subjects: Algebra; Algebraic Geometry; Automorphisms; Convex and Discrete Geometry; Geometry; Mathematics; Mathematics and Statistics; Original Paper; Clifford-like parallelism; 51J15; Automorphism; Kinematic algebra; Projective double space; Clifford parallelism; 51A15
• ISSN: 0138-4821; 2191-0383
• DOI: 10.1007/s13366-020-00509-4

We recall the notions of
Clifford
and
Clifford-like
parallelisms in a 3-dimensional projective double space. In a previous paper the authors proved that the linear part of the full automorphism group of a Clifford parallelism is the same for all Clifford-like parallelisms which can be associated to it. In this paper, instead, we study the action of such group on parallel classes thus achieving our main results on characterisation of the Clifford parallelisms among Clifford-like ones.