  We prove that a radial Kaehler metric g is Kaehler-Einstein if and only if
one of the following conditions is satisfied: 1. g is extremal and it is
associated to a Kaehler-Ricci soliton; 2. two different generalized scalar
curvatures of g are constant; 3. g is extremal (not cscK) and one of its
generalized scalar curvature is constant.
