2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77929This is the fourth of a series of papers studying real algebraic threefolds, but the methods are mostly independent from the previous ones. Let $f:X\to C$ be a map of a smooth projective real algebraic 3-fold to a curve $C$ whose general fibers are rational surfaces. 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 $M$.LATEX2e, 32 pagesAlgebraic Geometrytext