Geodesic
Constant Jacobi osculating rank of $\mathbf{U(3)/(U(1) \times U(1) \times U(1))}$
Archivum mathematicum, Tome 45 (2009) no. 4, pp. 241-254.

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In this paper 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.
Classification : 53C20, 53C21, 53C22, 53C25, 53C30
Keywords: naturally reductive space; g.o. space; Jacobi operator; Jacobi osculating rank 
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     author = {Arias-Marco, Teresa},
     title = {Constant {Jacobi} osculating rank of $\mathbf{U(3)/(U(1) \times U(1) \times U(1))}$},
     journal = {Archivum mathematicum},
     pages = {241--254},
     publisher = {mathdoc},
     volume = {45},
     number = {4},
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     mrnumber = {2591679},
     zbl = {1212.53059},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2009__45_4_a1/}
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Arias-Marco, Teresa. Constant Jacobi osculating rank of $\mathbf{U(3)/(U(1) \times U(1) \times U(1))}$. Archivum mathematicum, Tome 45 (2009) no. 4, pp. 241-254. http://geodesic.mathdoc.fr/item/ARM_2009__45_4_a1/