DOI QR코드

DOI QR Code

LEFT-INVARIANT MINIMAL UNIT VECTOR FIELDS ON A LIE GROUP OF CONSTANT NEGATIVE SECTIONAL CURVATURE

Yi, Seung-Hun

  • Published : 2009.07.31

Abstract

We find all left-invariant minimal unit vector fields and strongly normal unit vector fields on a Lie group which is isometric to the hyperbolic space.

Keywords

left-invariant minimal unit vector field;Lie group;hyperbolic manifold

References

  1. E. Boeckx and L. Vanhecke, Harmonic and minimal radial vector fields, Acta Math. Hungar. 90 (2001), no. 4, 317–331 https://doi.org/10.1023/A:1010687231629
  2. E. Boeckx and L. Vanhecke, Harmonic and minimal vector fields on tangent and unit tangent bundles, Differential Geom. Appl. 13 (2000), no. 1, 77–93 https://doi.org/10.1016/S0926-2245(00)00021-8
  3. O. Gil-Medriano and E. Llinares-Fuster, Second variation of volume and energy of vector fields. Stability of Hopf vector fields, Math. Ann. 320 (2001), no. 3, 531–545 https://doi.org/10.1007/PL00004485
  4. J. C. Gonzalez-Davila and L. Vanhecke, Minimal and harmonic characteristic vector fields on three-dimensional contact metric manifolds, J. Geom. 72 (2001), no. 1-2, 65–76 https://doi.org/10.1007/s00022-001-8570-4
  5. H. Gluck and W. Ziller, On the volume of a unit vector field on the three-sphere, Comment. Math. Helv. 61 (1986), no. 2, 177–192 https://doi.org/10.1007/BF02621910
  6. D. L. Johnson, Volumes of flows, Proc. Amer. Math. Soc. 104 (1988), no. 3, 923–931
  7. J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293–329 https://doi.org/10.1016/S0001-8708(76)80002-3
  8. S. L. Pedersen, Volumes of vector fields on spheres, Trans. Amer. Math. Soc. 336 (1993), no. 1, 69–78
  9. W. A. Poor, Differential Geometric Structures, McGraw-Hill Book Co., New York, 1981
  10. K. Tsukada and L. Vanhecke, Invariant minimal unit vector fields on Lie groups, Period. Math. Hungar. 40 (2000), no. 2, 123–133 https://doi.org/10.1023/A:1010331408580
  11. O. Gil-Medriano and E. Llinares-Fuster, Minimal unit vector fields, Tohoku Math. J. (2) 54 (2002), no. 1, 71–84 https://doi.org/10.2748/tmj/1113247180
  12. J. C. Gonzalez-Davila and L. Vanhecke, Examples of minimal unit vector fields, Ann. Global Anal. Geom. 18 (2000), no. 3-4, 385–404 https://doi.org/10.1023/A:1006788819180
  13. M. Salvai, On the volume of unit vector fields on a compact semi-simple lie group, Journal of Lie Theory 13 (2003), 455–462

Cited by

  1. LEFT-INVARIANT MINIMAL UNIT VECTOR FIELDS ON THE SEMI-DIRECT PRODUCT Rn vol.47, pp.5, 2010, https://doi.org/10.4134/BKMS.2010.47.5.951