Constant Jacobi osculating rank of $U(3)/(U(1) \times U(1) \times U(1))$ - Appendix -

Details Constant Jacobi osculating rank of $U(3)/(U(1) \times U(1) \times U(1))$ - Appendix - Constant Jacobi osculating rank of $U(3)/(U(1) \times U(1) \times U(1))$ - Appendix -

2009-06-16

arxiv.org/abs/0906.2890v2

Mathematics

Differential Geometry

7 pages

Scientific paper

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.

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