Results in Mathematics

, Volume 40, Issue 1–4, pp 226–232 | Cite as

Characterization of the Transformation Group of the Space of a Null System



In the space Ir of the invariant r-dimensional subspaces of a null system in (2r +1)-dimensional projective space, W.L. Chow characterized the basic group of transformations of Ir as all the transformations φ: Ir → Ir which are bijective and such that φ and φ−1 preserve adjacency. In the present paper we examine arbitrary mappings φ of Ir which satisfy the two conditions: 1. φ preserves adjacency. 2. For any a ∈ Ir there exists b ∈ Ir such that aφ ∩ bφ = ø.

1991 Mathematics subject classification

51A50 51B25 

Key words and phrases

Null system mappings preserving adjacency distance preserving mappings Lie geometry 


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Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  1. 1.Fachbereich Mathematik der Universität HamburgHamburgGermany

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