Stability of the geodesic flow for the energy

Eric Boeckx; José Carmelo González-Dávila; Lieven Vanhecke

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 2, page 201-213
  • ISSN: 0010-2628

Abstract

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We study the stability of the geodesic flow ξ as a critical point for the energy functional when the base space is a compact orientable quotient of a two-point homogeneous space.

How to cite

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Boeckx, Eric, González-Dávila, José Carmelo, and Vanhecke, Lieven. "Stability of the geodesic flow for the energy." Commentationes Mathematicae Universitatis Carolinae 43.2 (2002): 201-213. <http://eudml.org/doc/248991>.

@article{Boeckx2002,
abstract = {We study the stability of the geodesic flow $\xi $ as a critical point for the energy functional when the base space is a compact orientable quotient of a two-point homogeneous space.},
author = {Boeckx, Eric, González-Dávila, José Carmelo, Vanhecke, Lieven},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {geodesic flow; two-point homogeneous spaces; harmonic maps; stability; energy functional; geodesic flow; two-point homogeneous spaces; harmonic maps; stability; energy functional},
language = {eng},
number = {2},
pages = {201-213},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Stability of the geodesic flow for the energy},
url = {http://eudml.org/doc/248991},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Boeckx, Eric
AU - González-Dávila, José Carmelo
AU - Vanhecke, Lieven
TI - Stability of the geodesic flow for the energy
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 2
SP - 201
EP - 213
AB - We study the stability of the geodesic flow $\xi $ as a critical point for the energy functional when the base space is a compact orientable quotient of a two-point homogeneous space.
LA - eng
KW - geodesic flow; two-point homogeneous spaces; harmonic maps; stability; energy functional; geodesic flow; two-point homogeneous spaces; harmonic maps; stability; energy functional
UR - http://eudml.org/doc/248991
ER -

References

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  8. Higuchi A., Kay B.S., Wood C.M., The energy of unit vector fields on the 3 -sphere, J. Geom. Phys. 37 (2002), 137-155. (2002) MR1807086
  9. Milnor J., Curvature of left invariant metrics on Lie groups, Adv. in Math. 21 (1976), 293-329. (1976) MR0425012
  10. Tricerri F., Vanhecke L., Homogeneous Structures on Riemannian Manifolds, Lecture Note Series London Math. Soc. 83, Cambridge Univ. Press, 1983. Zbl0641.53047MR0712664
  11. Watanabe Y., Integral inequalities in compact orientable manifolds, Riemannian or Kählerian, Kōdai Math. Sem. Rep. 20 (1968), 264-271. (1968) MR0248702
  12. Wiegmink G., Total bending of vector fields on Riemannian manifolds, Math. Ann. 303 (1995), 325-344. (1995) Zbl0834.53034MR1348803
  13. Wiegmink G., Total bending of vector fields on the sphere S 3 , Differential Geom. Appl. 6 (1996), 219-236. (1996) MR1408308
  14. Wood C.M., On the energy of a unit vector field, Geom. Dedicata 64 (1997), 319-330. (1997) Zbl0878.58017MR1440565

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