  Let $\Omega$ be an unbounded two dimensional strip on a ruled surface in
$\mathbb{R}^d$, $d\geq2$. Consider the Laplacian operator in $\Omega$ with
Dirichlet and Neumann boundary conditions on opposite sides of $\Omega$. We
prove some results on the existence and absence of the discrete spectrum of the
operator; which are influenced by the twisted and bent effects of $\Omega$.
Provided that $\Omega$ is thin enough, we show an asymptotic behavior of the
eigenvalues. The interest in those considerations lies on the difference from
the purely Dirichlet case. Finally, we perform an appropriate dilatation in
$\Omega$ and we compare the results.
