Constant Jacobi osculating rank of

Teresa Arias-Marco

Archivum Mathematicum (2009)

  • Volume: 045, Issue: 4, page 241-254
  • ISSN: 0044-8753

Abstract

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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 . 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.

How to cite

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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 045.4 (2009): 241-254. <http://eudml.org/doc/261052>.

@article{Arias2009,
abstract = {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.},
author = {Arias-Marco, Teresa},
journal = {Archivum Mathematicum},
keywords = {naturally reductive space; g.o. space; Jacobi operator; Jacobi osculating rank; naturally reductive space; g.o. space; Jacobi operator; Jacobi osculating rank},
language = {eng},
number = {4},
pages = {241-254},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Constant Jacobi osculating rank of $\mathbf \{U(3)/(U(1) \times U(1) \times U(1))\}$},
url = {http://eudml.org/doc/261052},
volume = {045},
year = {2009},
}

TY - JOUR
AU - Arias-Marco, Teresa
TI - Constant Jacobi osculating rank of $\mathbf {U(3)/(U(1) \times U(1) \times U(1))}$
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 4
SP - 241
EP - 254
AB - 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.
LA - eng
KW - naturally reductive space; g.o. space; Jacobi operator; Jacobi osculating rank; naturally reductive space; g.o. space; Jacobi operator; Jacobi osculating rank
UR - http://eudml.org/doc/261052
ER -

References

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  1. Arias-Marco, T., Constant Jacobi osculating rank of -Appendix-, ArXiv:0906.2890v1. MR2591679
  2. Arias-Marco, T., Study of homogeneous D’Atri spaces of the Jacobi operator on g.o. spaces and the locally homogeneous connections on 2-dimensional manifolds with the help of Mathematica, thematica, Universitat de València, Valencia, Spain, 2007, ISBN: 978-84-370-6838-1, http://www.tdx.cat/TDX-0911108-110640. (2007) 
  3. Arias-Marco, T., Methods for solving the Jacobi equation. Constant osculating rank vs. constant Jacobi osculating rank, Differential Geometry Proceedings of the VIII International Colloquium, 2009, pp. 207–216. (2009) Zbl1180.53042MR2523506
  4. Arias-Marco, T., Naveira, A. M., Constant Jacobi osculating rank of a g.o. space. A method to obtain explicitly the Jacobi operator, Publ. Math. Debrecen 74 (2009), 135–157. (2009) Zbl1199.53111MR2490427
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  8. Kowalski, O., Prüfer, F., Vanhecke, L., D’Atri spaces, Progr. Nonlinear Differential Equations Appl. 20 (1996), 241–284. (1996) MR1390318
  9. Macías-Virgós, E., Naveira, A. M., Tarrío, A., 10.1016/j.crma.2007.11.009, C. R. Acad. Sci. Paris, Ser. I. Math. 346 (2008), 67–70. (2008) Zbl1134.53025MR2385057DOI10.1016/j.crma.2007.11.009
  10. Naveira, A. M., Tarrío, A., 10.1007/s00605-008-0551-3, Monatsh. Math. 158 (3) (2008), 231–246. (2008) Zbl1152.53039DOI10.1007/s00605-008-0551-3
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