Are there non-trivial diffeomorphisms of the complex projective plane that map geodesics (for the canonical Riemannian metric) to geodesics?

Same question for all other rank one symmetric spaces different from spheres and real projective spaces.

Are there non-trivial diffeomorphisms (i.e., different from isometries) of the complex projective plane that map geodesics (for the canonical Riemannian metric) to geodesics?

Same question for all other rank one symmetric spaces different from spheres and real projective spaces.