  We are interested in the spectrum of the Hodge-de Rham operator on a cyclic
covering $X$ over a compact manifold $M$ of dimension $n+1$. Let $\Sigma$ be a
hypersurface in $M$ which does not disconnect $M$ and such that $M-\Sigma$ is a
fundamental domain of the covering. If the cohomology group $H^{n/2 (\Sigma)$
is trivial, we can construct for each $N \in \N$ a metric $g=g_N$ on $M$, such
that the Hodge-de Rham operator on the covering $(X,g)$ has at least $N$ gaps
in its (essential) spectrum. If $H^{n/2}(\Sigma) \ne 0$, the same statement
holds true for the Hodge-de Rham operators on $p$-forms provided $p \notin
\{n/2,n/2+1\}$.

Differential Geometry