  We investigate spectral properties of the Laplace operator on a class of
non-compact Riemannian manifolds. For a given number $N$ we construct periodic
(i.e. covering) manifolds such that the essential spectrum of the corresponding
Laplacian has at least $N$ open gaps. We use two different methods. First, we
construct a periodic manifold starting from an infinite number of copies of a
compact manifold, connected by small cylinders. In the second construction we
begin with a periodic manifold which will be conformally deformed. In both
constructions, a decoupling of the different period cells is responsible for
the gaps.
