The zeta-determinants and anlaytic torsion of a metric mapping torus

We use the BFK-gluing formula for zeta-determinants to compute the zeta-determinant and analytic torsion of a metric mapping torus induced from an isometry. As applications, we compute the zeta-determinants of the Laplacians defined on a Klein bottle K and some compact co-K\"ahler manifold Tφ. We also show that a metric mapping torus and a Riemannian product manifold with a round circle have the same heat trace asymptotic expansions. We finally compute the analytic torsion of a metric mapping torus for the Witten deformed Laplacian and recover the result of J. Marcsik in {Ma}.