Vol. 17, No. 1, 2019
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A characterization of Clifford parallelism by automorphisms

Rainer Löwen
Vol. 17 (2019), No. 1, 43–46
DOI: 10.2140/iig.2019.17.43
Abstract

Betten and Riesinger have shown that Clifford parallelism on real projective space is the only topological parallelism that is left invariant by a group of dimension at least 5. We improve the bound to 4. Examples of different parallelisms admitting a group of dimension ≤ 3 are known, so 3 is the “critical dimension”.

Keywords
Clifford parallelism, automorphism group, topological parallelism
Mathematical Subject Classification 2010
Primary: 51H10, 51A15, 51M30
Milestones
Received: 17 February 2017
Accepted: 23 March 2017
Published: 19 November 2018
Authors
Rainer Löwen
Institut für Analysis und Algebra
Technische Universität Braunschweig
Braunschweig
Germany