Geodesic
On the hyperbolic unitary geometry
Journal of Algebraic Combinatorics, Tome 31 (2010) no. 4, pp. 547-583.

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Summary: Hans Cuypers (Preprint) describes a characterisation of the geometry on singular points and hyperbolic lines of a finite unitary space-the hyperbolic unitary geometry-using information about the planes. In the present article we describe an alternative local characterisation based on Cuypers' work and on a local recognition of the graph of hyperbolic lines with perpendicularity as adjacency. This paper can be viewed as the unitary analogue of the second author's article (J. Comb. Theory Ser. A 105:97-110, 2004) on the hyperbolic symplectic geometry.
Keywords: keywords hyperbolic unitary geometry, root group geometry, local recognition graphs, centralisers of involutions 
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Altmann, Kristina; Gramlich, Ralf. On the hyperbolic unitary geometry. Journal of Algebraic Combinatorics, Tome 31 (2010) no. 4, pp. 547-583. http://geodesic.mathdoc.fr/item/JAC_2010__31_4_a1/