Gluing formula of real analytic torsion forms and adiabatic limit

Abstract

In this paper we use the adiabatic limit method to prove the gluing formula of real analytic torsion forms for a flat vector bundle on a smooth fibration under the assumption that the fiberwise twisted cohomology groups of the gluing hypersurface are vanished. In this paper we assume that the metrics have product structures near the gluing hypersurface.