On the hyperbolic unitary geometry

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.