Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 43, No. 1, pp. 89-110 (2002)

Distance-preserving Maps in Generalized Polygons, I. Maps on Flags

Eline Govaert, Hendrik Van Maldeghem

University of Ghent, Pure Mathematics and Computer Algebra, Galglaan 2, 9000 Gent, Belgium e-mail: egovaert@@cage.rug.ac.be; hvm@@cage.rug.ac.be

Abstract: In this paper, we characterize isomorphisms of generalized polygons (in particular automorphisms) by maps on flags which preserve a certain fixed distance. In Part II, we consider maps on point and/or lines. Exceptions give rise to interesting properties, which on their turn have some nice applications.

Keywords: generalized polygons, distance-preserving maps

Classification (MSC2000): 51E12

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