Gauthier–Seshadri conjecture on rigidity of Kobayashi isometries

Let $M$ and $M'$ be Kobayashi hyperbolic complex manifolds. Let $f:(M,K_M)\to (M',K_{M'})$ be a Kobayashi isometry. If $M$ and $M'$ are not biholomorphic to a product of complex manifolds, then Gauthier–Seshadri's conjecture. $f$ is holomorphic or antiholomorphic.

The conjecture concerns when metric isometries between Kobayashi hyperbolic manifolds must respect the complex structure. It is known for certain classes of strongly convex bounded domains, but remains open in the stated generality.