  We prove stability and exponential convergence of the Perfectly Matched Layer
(PML) method for acoustic scattering on manifolds with axial analytic
quasicylindrical ends. These manifolds model long-range geometric perturbations
(e.g. bending or stretching) of tubular waveguides filled with homogeneous or
inhomogeneous media.
  We construct non-reflective infinite PMLs replacing the metric on a part of
the manifold by a non-degenerate complex symmetric tensor field. We prove that
the problem with PMLs of finite length is uniquely solvable and solutions to
this problem locally approximate scattered solutions with an error that
exponentially tends to zero as the length of PMLs tends to infinity.
