  For a compact 3-manifold $M$ which is a circle bundle over a compact Riemann
surface $\Sigma$ with even Euler number $e(M)$, and with a Riemannian metric
compatible with the bundle projection, there exists a compact minimal surface
$S$ in $M$. $S$ is embedded and is a section of the restriction of the bundle
to the complement of a finite number of points in $\Sigma$.
