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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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},
     year = {2009},
     volume = {45},
     number = {4},
     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/