Righteous isometries of weakly symmetric spaces

The concept of a righteous diffeomorphism of a Riemannian manifold is introduced. A righteous diffeomorphism of a manifold $M$ defines a weakly symmetric structure on $M$. For weakly symmetric Riemannian manifolds that are homogeneous spaces of semisimple Lie groups a complete classification of righteous diffeomorphisms (isometries) is obtained.