ASYMPTOTIC TORSION AND TOEPLITZ OPERATORS

We use Toeplitz operators to evaluate the leading term in the asymptotics of the analytic torsion forms associated with a family of flat vector bundles F-p. For p is an element of N, the flat vector bundle F-p is the direct image of L-p, where L is a holomorphic positive line bundle on the fibres of a flat fibration by compact Kahler manifolds. The leading term of the analytic torsion forms is the integral along the fibre of a locally defined differential form.