  This is the third of a series of papers studying real algebraic threefolds,
but the methods are mostly independent from the previous two. Let $f:X\to S$ be
a map of a smooth projective real algebraic 3-fold to a surface $S$ whose
general fibers are rational curves.
  Assume that the set of real points of $X$ is an orientable 3-manifold $M$.
The aim of the paper is to give a topological description of $M$. It is shown
that $M$ is either Seifert fibered or a connected sum of lens spaces. Much
stronger results hold if $S$ is rational.

Algebraic Geometry