Constant Jacobi osculating rank of U(3)/(U(1) x U(1) x U(1)) -- Appendix--

Abstract

Este es el apéndice del documento [T. Arias-Marco, Constant Jacobi osculating rank of U(3)/(U(1) × U(1) × U(1)), Arch. Math. (Brno) 45 (2009), 241–254]

This is the appendix of the paper [T. Arias-Marco, Constant Jacobi osculating rank of U(3)/(U(1) × U(1) × U(1)), Arch. Math. (Brno) 45 (2009), 241–254] where we obtain an interesting relation between the co-variant derivatives of the Jacobi operator valid for all geodesic on the flag manifold M6 = U(3)/(U(1)×U(1)×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.