Previous |  Up |  Next

Article

Title: Stability of the geodesic flow for the energy (English)
Author: Boeckx, E.
Author: González-Dávila, J. C.
Author: Vanhecke, L.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 43
Issue: 2
Year: 2002
Pages: 201-213
.
Category: math
.
Summary: 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. (English)
Keyword: geodesic flow
Keyword: two-point homogeneous spaces
Keyword: harmonic maps
Keyword: stability
Keyword: energy functional
MSC: 53C20
MSC: 53C22
MSC: 53C30
MSC: 58E20
idZBL: Zbl 1090.53035
idMR: MR1922122
.
Date available: 2009-01-08T19:21:12Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/119314
.
Reference: [1] Boeckx E., Vanhecke L.: Characteristic reflections on unit tangent sphere bundles.Houston J. Math. 23 (1997), 427-448. Zbl 0897.53010, MR 1690045
Reference: [2] Boeckx E., Vanhecke L.: Harmonic and minimal vector fields on tangent and unit tangent bundles.Differential Geom. Appl. 13 (2000), 77-93. Zbl 0973.53053, MR 1775222
Reference: [3] Borel A.: Compact Clifford-Klein forms of symmetric spaces.Topology 2 (1963), 111-122. Zbl 0116.38603, MR 0146301
Reference: [4] Brito F.: Total bending of flows with mean curvature correction.Differential Geom. Appl. 12 (2000), 157-163. Zbl 0995.53023, MR 1758847
Reference: [5] Chen B.Y., Vanhecke L.: Differential geometry of geodesic spheres.J. Reine Angew. Math. 25 (1981), 28-67. Zbl 0503.53013, MR 0618545
Reference: [6] González-Dávila J.C., Vanhecke L.: Energy and volume of unit vector fields on three-dimensional Riemannian manifolds.Differential Geom. Appl., to appear. MR 1900746
Reference: [7] Gray A., Vanhecke L.: Riemannian geometry as determined by the volumes of small geodesic balls.Acta Math. 142 (1979), 157-198. Zbl 0428.53017, MR 0521460
Reference: [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. MR 1807086
Reference: [9] Milnor J.: Curvature of left invariant metrics on Lie groups.Adv. in Math. 21 (1976), 293-329. MR 0425012
Reference: [10] Tricerri F., Vanhecke L.: Homogeneous Structures on Riemannian Manifolds.Lecture Note Series London Math. Soc. 83, Cambridge Univ. Press, 1983. Zbl 0641.53047, MR 0712664
Reference: [11] Watanabe Y.: Integral inequalities in compact orientable manifolds, Riemannian or Kählerian.Kōdai Math. Sem. Rep. 20 (1968), 264-271. MR 0248702
Reference: [12] Wiegmink G.: Total bending of vector fields on Riemannian manifolds.Math. Ann. 303 (1995), 325-344. Zbl 0834.53034, MR 1348803
Reference: [13] Wiegmink G.: Total bending of vector fields on the sphere $S^3$.Differential Geom. Appl. 6 (1996), 219-236. MR 1408308
Reference: [14] Wood C.M.: On the energy of a unit vector field.Geom. Dedicata 64 (1997), 319-330. Zbl 0878.58017, MR 1440565
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_43-2002-2_2.pdf 248.0Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo