Geometric Finiteness of Certain Kleinian Groups

If $G$ is a discrete subgroup of $\operatorname {PSL} \left ( {2;{\mathbf {C}}} \right )$ representing a fibred $3$-manifold and $H$ the subgroup of $G$ corresponding to the fibre, we show that any finitely generated subgroup of infinite index in $H$ is geometrically finite.