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Hyperbolic lines in generalized polygons

In this paper we develop the theory of hyperbolic lines in generalized polygons. In particular, we investigate the extremal situation where hyperbolic lines are long. We give restrictions on the existence of long hyperbolic lines and characterize the symplectic generalized quadrangles W (k) and generalized hexagons H(k) related to the groups G2(k) by the existence of certain classes of long hyperbolic lines.