On smooth rationally connected projective threefolds of Picard number two admitting int-amplified endomorphisms

We prove that a smooth rationally connected projective threefold of Picard number two is toric if and only if it admits an int-amplified endomorphism. As a corollary, we show that a totally invariant smooth curve of a non-isomorphic surjective endomorphism of $\mathbb{P}^3$ must be a line when it is blowup-equivariant.