  In a recent preprint Yael Karshon showed that there exist non-conjugate tori
in a group of symplectomorphisms of a Hirzebruch surface. She counted them in
terms of the cohomology class of the symplectic structure. We show that a
similar phenomenon exists in the contactomorphism groups of pre-quantum circle
bundles over Hirzebruch surfaces. Note that the contact structures in question
are fillable. This may be contrasted with an earlier paper where we showed that
there are infinitely many non-conjugate tori in the contactomorphism groups of
certain overtwisted lens spaces (Contact cuts, Israel J. Math, 124(2001),
77--92).
