Algebraic fibre spaces with strictly nef relative anti‐log canonical divisor

Let be a projective klt pair, and a fibration to a smooth projective variety with strictly nef relative anti‐log canonical divisor . We prove that is a locally trivial fibration with rationally connected fibres, and the base is a canonically polarized hyperbolic manifold. In particular, when is a single point, we establish that is rationally connected. Moreover, when and is strictly nef, we prove that is ample, which confirms the singular version of a conjecture by Campana and Peternell for threefolds.