  This is the appendix of the paper [T. Arias-Marco, Constant Jacobi osculating
rank of $U(3)/(U(1) \times U(1) \times U(1))$, Arch. Math. (Brno) 45 (2009),
241--254] where we obtain an interesting relation between the covariant
derivatives of the Jacobi operator valid for all geodesic on the flag manifold
$M^6=U(3)/(U(1) \times U(1) \times U(1))$. As a consequence, an explicit
expression of the Jacobi operator independent of the geodesic can be obtained
on such a manifold. Moreover, we show the way to calculate the Jacobi vector
fields on this manifold by a new formula valid on every g.o. space.
