Let $X$ be a Fano manifold with $b_2=1$ different from the projective space such that any two surfaces in $X$ have proportional fundamental classes in $H_4(X,\mathbf{C})$. Let $f:Y\to X$ be a surjective holomorphic map from a projective variety $Y$. We show that all deformations of $f$ with $Y$ and $X$ fixed, come from automorphisms of $X$. The proof is obtained by studying the geometry of the integral varieties of the multi-valued foliation defined by the variety of minimal rational tangents of $X$.