  Self dual symmetric R-spaces have special curves, called circles, introduced
by Burstall, Donaldson, Pedit and Pinkall in 2011, whose definition does not
involve the choice of any Riemannian metric. We characterize the elements of
the big transformation group G of a self dual symmetric R-space M as those
diffeomorphisms of M sending circles in circles. Besides, although these curves
belong to the realm of the invariants by G, we manage to describe them in
Riemannian geometric terms: Given a circle c in M, there is a maximal compact
subgroup K of G such that c, except for a projective reparametrization, is a
diametrical geodesic in M (or equivalently, a diagonal geodesic in a maximal
totally geodesic flat torus of M), provided that M carries the canonical
symmetric K-invariant metric. We include examples for the complex quadric and
the split standard or isotropic Grassmannians.
