Surjective endomorphism conjecture for Fano manifolds of Picard number one

Let $X$ be a Fano manifold of Picard number one, meaning that its Picard number is one, and suppose that $X$ is different from the projective space. A surjective endomorphism is a morphism $f:X\to X$ that is surjective.

Surjective endomorphism conjecture. Every surjective endomorphism $f:X\to X$ must be bijective.

This conjecture concerns the rigidity of self-maps of Fano manifolds with Picard number one. It is still open in general, but has been affirmatively solved in dimensions at most $3$.