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
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